function posts_by_year() {
  // array to use for results
  $years = array();

  // get posts from WP
  $posts = get_posts(array(
    'numberposts' => -1,
    'orderby' => 'post_date',
    'order' => 'ASC',
    'post_type' => 'my-custom-post-type',
    'post_status' => 'publish'
  ));

  // loop through posts, populating $years arrays
  foreach($posts as $post) {
    $years[date('Y', strtotime($post->post_date))][] = $post;
  }

  // reverse sort by year
  krsort($years);
  return $years;
}

<?php foreach(posts_by_year() as $year => $posts) : ?>
<h2><?php echo $year; ?></h2>
// the code that I need to display the post counts per year
<?php endforeach; ?>