How can I display my custom posts type in a monthly calendar view?

I am looking for a way to display my Custom Post Type posts in a full-page monthly calendar type display (like what you see in Google calendar). Ideally, the calendar would be dynamic in which user could click from month to month. And I would want the actual post titles to be displayed and linked in the squares.

I know there are a multitude of "event calendar" plugins, but that is not what I am looking for. I want to control the content type that is displayed. There is also the built-in Calendar widget but that seems way too basic and I can't see a way of filtering by content type.

This is the sort of thing that I could do very easily in Drupal with the views calendar module, but I am at a loss at how to achieve this display in Wordpress.

I am hoping there is a plugin that can accomplish this, but I am open to coded solutions.