In the work bowl of a food processor combine the flour, cocoa powder, cornstarch, brown sugar, and salt. Pulse 5 times to combine. Add the cubed butter and pulse until the mixture looks like coarse sand, about 12 times pulses. Add the cream cheese, milk, and vanilla and pulse until the dough forms a smooth ball, about 15 pulses.
Turn the dough out onto a lightly floured surface and divide into 30 pieces. Roll each piece into a ball and place them into a non-stick mini-muffin pan. Using a dough tamper, or your fingers, press each ball into a cup shape. Cover with plastic and chill for one hour.
Heat the oven to 350 F. Once the dough has chilled remove the plastic and bake for 13 to 16 minutes, or until the cookies are firm when pressed. Cool for 5 minutes in the pan, then transfer to a wire rack to cool to room temperature.
Now, prepare the frosting.
In a medium pot over medium heat add the butter. Cook, stirring constantly, until the butter browns and smells nutty. Cool the butter completely to room temperature.
Once the butter has cooled add it into the work bowl of a stand mixer fitted with the paddle attachment (or in a medium bowl with a hand mixer) along with 3 cups of the powdered sugar, espresso, milk, vanilla, and a pinch of salt. Mix on low speed until the mixture is smooth. Add more powdered sugar one tablespoon at a time until the mixture is medium stiffness - meaning it holds a peak when you remove the paddle.
To assemble the cookies begin by melting the chocolate chips. Place them in a shallow microwave safe bowl. Heat the chips for 30 seconds then stir. If the chips are not melted (and at this point they will not be) return them to the microwave for 12 second intervals until they are melted and smooth.
Dip the top edge of the cookie cups into the melted chocolate, letting any excess drip off, then directly into the crushed peppermint. Pipe, or spoon, the buttercream into the cups and top with colored sprinkles. Chill for 30 minutes to set the chocolate before serving.
Recipe by Baking and Cooking Blog - Evil Shenanigans at http://www.evilshenanigans.com/2012/12/mocha-mint-cookie-cups/