Blog monthly archive block - list of posts grouped by year then month
It's normally done using Views and a good tutorial on the process has been explained by Chris Shattuck on his blog - see How to create a monthly archive block for a Drupal blog with Views

A little sleuthing on how the blog you mention was generated leads me to believe that the author wrote the wp_blog module on Drupal.org which provides a view that ultimately generates the year -> month -> post hierarchy.  You can see an exported view for the blog archive block here: http://cgit.drupalcode.org/wp_blog/tree/views/wp_blog.view?id=47246da29d176c028a749632807d207dfe0461e1