Add the following code to your Genesis Child theme functions.php file. Read the full guide here: https://wp-me.com/last-updated-date-post-meta-data-genesis/

functions.php

<?php // Ignore this line

/*
* Replace Post publish date with Post update date in Genesis
* More info: https://wp-me.com/last-updated-date-post-meta-data-genesis/
*/
add_filter( 'genesis_post_info', 'wpme_post_info_filter' );
function wpme_post_info_filter($post_info) {
  if ( !is_page() ) {
    $post_info = '[post_modified_date] ' . __( 'by', 'genesis' ) . ' [post_author_posts_link] [post_comments] [post_edit]';
    return $post_info;
  }
}

// Ignore this line ?>