In a medium sized bowl, melt the butter and chocolate stirring every 15 seconds. Once melted, set aside.
In another medium bowl, whisk together the flour, cocoa powder, baking powder, and salt.
In a large mixing bowl, beat the sugar, eggs, and vanilla on low speed with an electric mixer until well combined. Add the cooled chocolate and blend until just combined.
While mixing, add the flour mixture slowly, a cup at a time. Scrape the edges of the bowl as you go. Cover and refrigerate for 1 hour. The dough should be firm.
Preheat the oven to 325° and line two large baking sheets with parchment paper.
Grab a tablespoon-size of dough and roll into a ball, or using a cookie dough scooper, scoop a tablespoon worth. Flatten the dough ball out slightly with the bottom of a glass and place onto the baking sheet about 2 inches apart.
Bake the cookies for 9-11 minutes.
While the cookies are baking, cut the marshmallows in half crosswise. (Kitchen scissors are great for this.) Remove the cookies from the oven and place one half of the marshmallows, sticky side down, in the middle of the cookies.
Return the cookies to the oven and bake for another 2 minutes. Remove cookies and allow the cookies to cool for a few minutes and then transfer to a wire cooling rack.