In a large bowl, cream together the peanut butter, butter, white sugar, and brown sugar until well blended. Beat in egg, milk, and vanilla one at a time until well incorporated.
In a separate bowl combine flour, baking powder, and salt. Mix with wire whisk. Stir into creamed mixture. Roll, or scoop, tablespoons of dough into balls. Place cookies 2 inches apart onto parchment lined or silicone mat lined baking sheets.
Press a large teaspoon full of chopped Reese peanut butter cups into the top of each scoop of dough. Slightly press down each cookie.
Bake for 8-10 minutes in the preheated oven, switching baking racks half way through cook time, or until edges are lightly brown.
Remove from baking sheet and place on cooling rack. Store in air tight container.