Preheat the oven to 350 degrees F (175 degrees C).
Mix flour, sugar, and cocoa powder in a large bowl. Cut in butter until mixture resembles fine crumbs. Set aside 1 cup of the crumbs to be used as the topping. Press remaining crumb mixture into an ungreased 8x8-inch baking pan.
Bake crust in the preheated oven until set, about 15 minutes. Remove and let cool. Keep oven on.
While crust is cooling, beat cream cheese and sugar with an electric mixer until fluffy. Add egg, peppermint extract, and green food coloring; beat well. Stir in milk until batter is smooth. Pour batter over the cooled crust. Sprinkle reserved crumb mixture on top.
Bake until filling is set, 20 to 25 minutes. Cool before cutting into 25 bars.
