Extending TimberMenu

CustomMenu.php

<?php

/**
 * Custom Menu class to add special nav behavior on top of
 * TimberMenu instances.
 * 
 * Context: https://github.com/jarednova/timber/issues/808
 */
class CustomMenu extends \TimberMenu {
	public $MenuItemClass = '\CustomMenuItem';
}

CustomMenuItem.php

<?php

/**
 * Custom MenuItem class for adding special nav behavior to
 * TimberMenuItem instances
 */
class CustomMenuItem extends \TimberMenuItem {
	public function get_post() {
	  // Only want to look associated posts for items that are actually linked to posts,
	  // as opposed to custom link-type items...
		if( $this->type === 'post_type' ) {
			return new \TimberPost($this->object_id);
		}
	}
}

nav.twig

<nav class="side-nav level1">
	<ul class="menu">
		{% for item in menu.get_items() %}

			<li class="{{ item.classes | join(' ') }}">
			  {# now you can access the associated post via the item.get_post() method: #}
				<a href="{{ item.get_path }}">{{ item.get_post().get_field('whatever') }}</a>
			</li>

		{% endfor %}
	</ul>
</nav>