Whisk flour, cocoa powder, baking soda, baking powder, and salt together in a bowl.

Beat butter with an electric mixer until fluffy, about 2 minutes; beat in brown sugar and white sugar until smooth, about 1 minute. Beat egg, milk, and vanilla extract into butter mixture; beat in food coloring until uniformly colored.

Stir flour mixture into butter mixture gradually with electric mixer on low speed until combined; stir in 1 cup chocolate chips. Cover bowl with plastic wrap; place in the refrigerator for 1 hour or up to overnight.

Preheat oven to 350 degrees F (175 degrees C). Line baking sheets with parchment paper.

Roll dough into 2-inch balls; place on prepared baking sheets and flatten slightly.

Bake in the preheated oven until edges are lightly browned, about 10 minutes. Sprinkle cookies with a few additional chocolate chips; allow to cool completely.