MomentJsDateFormatHelper that I use with jknack's handlebars.java project.

MomentJsDateFormatHelper.java

import com.github.jknack.handlebars.Helper;
import com.github.jknack.handlebars.Options;
import org.jetbrains.annotations.NotNull;
import org.jetbrains.annotations.Nullable;

import javax.script.ScriptEngine;
import javax.script.ScriptEngineManager;
import javax.script.ScriptException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.Reader;
import java.util.Date;

public class MomentJsDateFormatHelper
   implements Helper<Date>
{
   // RAJ - This file must be in the root classpath (I stick it under src/main/resources and maven puts it where it needs to go)
   // RAJ - I am using v1.7.2, as the latest version doesn't set a global "moment" constructor correctly under Rhino
   // RAJ - You can find v1.7.2 here: https://raw.githubusercontent.com/moment/moment/1.7.2/moment.js
   @NotNull private static final String MOMENT_JS_FILE = "moment.js";

   @NotNull private final ScriptEngine m_momentJsScriptEngine = initializeScriptEngine( MOMENT_JS_FILE );

   @Override
   @NotNull
   public CharSequence apply (
      @NotNull Date date,
      @NotNull Options options )
      throws IOException
   {
      String format = options.param(0, options.<String>hash("format", null));
      return formatDate( date, format );
   }

/*
   @NotNull
   private synchronized String formatDate (
      @NotNull Date date,
      @Nullable String format )
   {
      try
      {
         Object moment = ( (Invocable)m_momentJsScriptEngine ).invokeFunction( "moment", date.getTime() );
         if( format == null )
            return ( (Invocable)m_momentJsScriptEngine ).invokeMethod( moment, "calendar" ).toString();

         String[] formatArgs = new String[] { format };
         // RAJ - It is probably cleaner to use Invocable instead of eval but this line always throws NPE under Java6
         return ( (Invocable)m_momentJsScriptEngine ).invokeMethod( moment, "format", formatArgs ).toString();
      }
      catch( ScriptException e )
      {
         throw new RuntimeException( "Failed to format date", e );
      }
      catch( NoSuchMethodException e )
      {
         throw new RuntimeException( "Failed to format date", e );
      }
   }
*/

   @NotNull
   private CharSequence formatDate (
      @NotNull Date date,
      @Nullable String format )
   {
      String javascript = getMomentJsFormattingJavascript( date, format );
      return evalJavascript( javascript );
   }

   @NotNull
   private String getMomentJsFormattingJavascript (
      @NotNull Date date,
      @Nullable String format )
   {
      if( format == null )
         return "new moment(" + date.getTime() + ").calendar();";
      format = format.replace( "'", "\\'" );
      return "new moment(" + date.getTime() + ").format('" + format + "');";
   }

   @NotNull
   private static ScriptEngine initializeScriptEngine ( @NotNull String momentJsFile)
   {
      InputStream is = Thread.currentThread().getContextClassLoader().getResourceAsStream( momentJsFile );
      Reader reader = new InputStreamReader( is );
      ScriptEngineManager manager = new ScriptEngineManager();
      ScriptEngine engine = manager.getEngineByName( "JavaScript" );
      try
      {
         engine.eval( reader );
         // RAJ - Since I'm only concerned about my own locale, I don't worry about it but you may want to load
         //       any locale data you care about here...
         return engine;
      }
      catch( ScriptException e )
      {
         throw new RuntimeException( e );
      }
   }

   // RAJ - I have no idea how thread safe the Rhino code is, so I'm synchronizing this method just to be safe
   @NotNull
   private synchronized String evalJavascript ( @NotNull String script )
   {
      try
      {
         return m_momentJsScriptEngine.eval( script ).toString();
      }
      catch( ScriptException e )
      {
         throw new RuntimeException( e );
      }
   }
}

MomentJsDateFormatHelperTest.java

import com.github.jknack.handlebars.Context;
import com.github.jknack.handlebars.Handlebars;
import com.github.jknack.handlebars.Template;
import com.github.jknack.handlebars.context.MapValueResolver;
import junit.framework.Assert;
import org.apache.commons.lang3.StringEscapeUtils;
import org.junit.Test;

import java.io.IOException;
import java.text.ParseException;
import java.text.SimpleDateFormat;
import java.util.Collections;
import java.util.Date;

public class MomentJsDateFormatHelperTest
{
   @Test
   public void testMomentJsDateFormatting ()
      throws IOException, ParseException
   {
      SimpleDateFormat sdf = new SimpleDateFormat( "yyyy-MM-dd hh:mm:ss a" );
      Date date = sdf.parse( "2014-10-01 12:32:23 PM" );
      Template template = compileTemplate( "date is {{dateFormat date format='MMMM Do, YYYY [at] hh:mm a [and] ss [seconds]'}}" );
      Context context = createContext( Collections.singletonMap( "date", date ) );
      Assert.assertEquals( "date is October 1st, 2014 at 12:32 pm and 23 seconds", template.apply( context ) );
   }

   @Test
   // RAJ - internally we evaluate the javascript inline using single quotes to surround the format
   public void testFormatIncludingQuotes1 ()
      throws IOException, ParseException
   {
      SimpleDateFormat sdf = new SimpleDateFormat( "yyyy-MM-dd hh:mm:ss a" );
      Date date = sdf.parse( "2014-10-01 12:32:23 PM" );
      Template template = compileTemplate( "date is {{dateFormat date format='MMMM Do, [\\']YY [\"yay\"]'}}" );
      Context context = createContext( Collections.singletonMap( "date", date ) );
      // RAJ - By default, Handlebars escapes text for HTML and we have quotes in our generated output
      String htmlEscapedText = template.apply( context );
      String unescapedText = StringEscapeUtils.unescapeHtml4( htmlEscapedText );
      Assert.assertEquals( "date is October 1st, '14 \"yay\"", unescapedText );
   }

   @Test
   // RAJ - internally we evaluate the javascript inline using single quotes to surround the format
   public void testFormatIncludingQuotes2 ()
      throws IOException, ParseException
   {
      SimpleDateFormat sdf = new SimpleDateFormat( "yyyy-MM-dd hh:mm:ss a" );
      Date date = sdf.parse( "2014-10-01 12:32:23 PM" );
      Template template = compileTemplate( "date is {{dateFormat date format=\"MMMM Do, [']YY [\\\"yay\\\"]\"}}" );
      Context context = createContext( Collections.singletonMap( "date", date ) );
      // RAJ - By default, Handlebars escapes text for HTML and we have quotes in our generated output
      String htmlEscapedText = template.apply( context );
      String unescapedText = StringEscapeUtils.unescapeHtml4( htmlEscapedText );
      Assert.assertEquals( "date is October 1st, '14 \"yay\"", unescapedText );
   }

   @Test
   public void testFormatAndEmptyFormatString ()
      throws IOException, ParseException
   {
      SimpleDateFormat sdf = new SimpleDateFormat( "yyyy-MM-dd hh:mm:ss a" );
      Date date = sdf.parse( "2014-10-01 12:32:23 PM" );
      Template template = compileTemplate( "date is {{dateFormat date}}" );
      Context context = createContext( Collections.singletonMap( "date", date ) );
      // RAJ - I have no idea how this should behave under non-US locales, so I'm not sure how useful this assertion is
      // RAJ - We should probably just check to make sure that something was generated here, rather than the specific format
      // RAJ - Then again, all of the MMMM stuff above is also locale (language) specific...
      Assert.assertEquals( "date is 10/01/2014", template.apply( context ) );
   }

   private Context createContext ( Object data )
   {
      return Context.newBuilder( data )
         .resolver( MapValueResolver.INSTANCE )
         .build();
   }

   private Template compileTemplate ( String templateText )
      throws IOException
   {
      Handlebars handlebars = new Handlebars();
      handlebars.registerHelper( "dateFormat", new MomentJsDateFormatHelper() );
      return handlebars.compileInline( templateText );
   }
}

I based this gist off of another gist from UnquietCode that you can find here.