Source code for https://victorfont.com/genesis-mobile-responsive-custom-menu-widget/

genesis_header_menu_wrap.php

<?php

function genesis_header_menu_wrap( $menu ) {

	if ( ! genesis_html5() )
		return $menu;

	return sprintf( '<nav>', genesis_attr( 'nav-header' ) ) . $menu . '</nav>';
}

vmf_custom_responsive_menu.php

<?php
	
add_action( 'genesis_before_header', 'vmf_custom_responsive_menu' );
function vmf_custom_responsive_menu() {

	remove_action( 'genesis_header', 'genesis_do_header' );
	add_action( 'genesis_header', 'vmf_genesis_do_responsive_header' );

}

function vmf_genesis_do_responsive_header() {
	global $wp_registered_sidebars;

	genesis_markup( array( 
		'html5' => '<div>', 
		'xhtml' => '<div id="title-area">', 'context' => 'title-area', ) );
		
	do_action( 'genesis_site_title' );
	do_action( 'genesis_site_description' );
	echo '</div>';
	
	if ( ( isset( $wp_registered_sidebars['header-right'] ) && is_active_sidebar( 'header-right' ) ) || has_action( 'genesis_header_right' ) ) {
		genesis_markup( array(
			'html5' => '<aside>',
			'xhtml' => '<div class="widget-area header-widget-area">',
			'context' => 'header-widget-area', ) );
		
		do_action( 'genesis_header_right' );
		add_filter( 'wp_nav_menu_args', 'genesis_header_menu_args' );
		add_filter( 'wp_nav_menu', 'vmf_genesis_header_menu_wrap' );
		dynamic_sidebar( 'header-right' );
		remove_filter( 'wp_nav_menu_args', 'genesis_header_menu_args' );
		remove_filter( 'wp_nav_menu', 'vmf_genesis_header_menu_wrap' );
		genesis_markup( array(
			'html5' => '</div></aside>',
			'xhtml' => '</div>',
		) );
	}
}

function vmf_genesis_header_menu_wrap( $menu ) {

	if ( ! genesis_html5() )
		return $menu;

		$responsive = '<div class="responsive-primary-menu-container">';
		$responsive .= '<div class="responsive-menu-icon">';
		$responsive .= '   ';
		$responsive .= '</div>';
		$responsive .= '<h3 class="mobile-primary-toggle">Navigation</h3>';
		$responsive .= '</div>';
}