Preheat oven to 350 degrees F (175 degrees C). Grease a 10x13-inch baking dish.
Mix flour, sugar, butter, eggs, milk, coffee-flavored liqueur, brewed coffee, cocoa powder, vanilla extract, baking powder, and baking soda together in the bowl of a stand mixer; beat until smooth. Spread batter into prepared baking dish.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 20 minutes. Cool 10 minutes before cutting to serve.