Preheat the oven to 375 degrees F (190 degrees C). Sift together flour, baking soda, baking powder, and salt. Set aside.

Cream together butter, sugar, and brown sugar in a large bowl. Mix in vanilla extract and cocoa powder, then add peanut butter, and stir until smooth. Gradually mix in the sifted ingredients until well blended. Pour milk into dough, and stir until fully combined.

Drop dough by heaping teaspoons onto ungreased baking sheets. Bake in the preheated oven until edges are lightly browned, 11 to 13 minutes. For a crunchier cookie, bake an additional minute or two.