Wordpress - Get all authors with at least one post of 'custom post type'

For now post_type support is not currently available for count_user_posts(),

so put the below code in theme's functions.php file.

function count_user_posts_by_type( $userid, $post_type = 'post' ) {
    global $wpdb;
    $where = get_posts_by_author_sql( $post_type, true, $userid );
    $count = $wpdb->get_var( "SELECT COUNT(*) FROM $wpdb->posts $where" );
    return apply_filters( 'get_usernumposts', $count, $userid );
}

Now this function would take user id and post_type as parameter post_type='post' being the default and gets the count of post for that user for the concerned post_type

You can verify it by echoing the below where you need to check the post count by the user.

$user_posts = count_user_posts_by_type( 1, 'page' );
echo $user_posts; // This would return the post count for user id 1 and post_type page.

You can do the same for the custom post type. Now you need to get the user ids and pass through this function and display the name of the authors having 1 or more posts or

You can add the below code where you want to display the list of users with one or more post

$blogusers = get_users();
foreach ( $blogusers as $user ) {
    if ( count_user_posts_by_type( $user->ID, 'post') ) {
         echo $user->user_nicename . '</br>';
    }
}

The above code lists all the users with one or more posts published of post_type post.