Preheat the oven to 350°F (180°C). Grease a 24 count mini muffin pan. This recipe makes 15-18 cookie cups.
In a medium sized bowl, whisk flour, cocoa powder, baking soda, cornstarch, and salt together. Set aside.
Mix butter, granulated sugar, and brown sugar together in a large bowl until well combined, about 3 minutes of mixing.
Add egg and vanilla, and mix until combined. Scrape down the sides of the bowl as needed. Add the dry ingredients and mix until everything is combined.
Form dough into 1 inch balls and place each one in the prepared mini muffin pan. Use your thumb to press the center down to make a slight indention. This is where you will add the buttercream filling later.
Bake for 7-9 minutes, or until the centers are a touch underdone. Don't overbake. The cookies will cook more as they sit at room temperature.
Use a tablespoon or the end of a wooden spoon to press the centers down to fit buttercream in it. Let cool for 15 minutes in the muffin pan, then remove to a cooling rack to cool completely.