In a large bowl, whisk together flour, cocoa, baking powder, baking soda and salt.
In a stand mixer, beat butter with sugar until very fluffy, 3 minutes, scraping down sides occasionally. Beat in eggs and then vanilla extract. Remove bowl from mixer and stir in chocolate and graham crackers (reserving a small handful of each for topping, if you like).
Refrigerate dough for 30 minutes (or up to 24 hours). Meanwhile, preheat oven to 375ºF and line baking sheets with parchment paper. Scoop dough by two-tablespoonfuls and roll between palms to form a nice ball. Space about two inches apart on prepared baking sheets. Make a slight indent in the top of each and place a marshmallow half in the indent (as well as reserved chopped chocolate and graham cracker, if you're feeling fancy).
Bake cookies for 8-10 minutes, until a few cracks appear, edges have lost their shine, and marshmallow is a bit toasty. Let cool for 2 minutes on baking sheets before transferring to wire racks to cool completely.