CookieExample.csproj

<Project Sdk="Microsoft.NET.Sdk.Web">

  <PropertyGroup>
    <TargetFramework>netcoreapp1.1</TargetFramework>
  </PropertyGroup>

  <ItemGroup>
    <Folder Include="wwwroot\" />
  </ItemGroup>
  <ItemGroup>
    <PackageReference Include="Microsoft.ApplicationInsights.AspNetCore" Version="2.0.0" />
    <PackageReference Include="Microsoft.AspNetCore" Version="1.1.1" />
    <PackageReference Include="Microsoft.AspNetCore.Authentication" Version="1.1.2" />
    <PackageReference Include="Microsoft.AspNetCore.Authentication.Cookies" Version="1.1.2" />
  </ItemGroup>

</Project>

Program.cs

using System.IO;
using Microsoft.AspNetCore.Hosting;

namespace CookieExample
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var host = new WebHostBuilder()
                .UseKestrel()
                .UseContentRoot(Directory.GetCurrentDirectory())
                .UseIISIntegration()
                .UseStartup<Startup>()
                .UseApplicationInsights()
                .Build();

            host.Run();
        }
    }
}

Startup.cs

using System;
using System.Security.Claims;
using Microsoft.AspNetCore.Builder;
using Microsoft.AspNetCore.Hosting;
using Microsoft.AspNetCore.Http;
using Microsoft.Extensions.DependencyInjection;
using Microsoft.Extensions.Logging;
using Microsoft.AspNetCore.Authentication.Cookies;

namespace CookieExample
{
    public class Startup
    {
        public void ConfigureServices(IServiceCollection services)
        {
            services.AddAuthentication();
        }

        public void Configure(IApplicationBuilder app, IHostingEnvironment env, ILoggerFactory loggerFactory)
        {
            loggerFactory.AddConsole();

            app.UseDeveloperExceptionPage();
            app.Use(async (ctx, next) =>
            {
                if (ctx.Request.Path == "/favicon.ico")
                {
                    ctx.Response.StatusCode = 404;
                    return;
                }

                await next.Invoke();
            });

            app.UseCookieAuthentication(new CookieAuthenticationOptions
            {
                LoginPath = new PathString("/login"),
                LogoutPath = new PathString("/logout"),
                ExpireTimeSpan = TimeSpan.FromMinutes(1),
                SlidingExpiration = true
            });

            app.Run(async context =>
            { 
                if (context.Request.Path == "/login")
                {
                    var identity = new ClaimsIdentity(new Claim[0], CookieAuthenticationDefaults.AuthenticationScheme);
                    await context.Authentication.SignInAsync(CookieAuthenticationDefaults.AuthenticationScheme, new ClaimsPrincipal(identity));
                    await context.Response.WriteAsync("Signed in");
                    return;
                }

                var status = "authenticated? " + context.User.Identity.IsAuthenticated;

                if (context.Request.Path == "/exception")
                {
                    throw new Exception(status);
                    
                }

                await context.Response.WriteAsync(status);
            });
        }
    }
}