Preheat oven to 375 degrees F (190 degrees C). Sift all-purpose flour, whole-wheat flour, baking soda, and salt.
Beat butter, white sugar, brown sugar, and peanut butter with an electric mixer in a large bowl until smooth. Add egg allowing to blend into butter mixture. Beat in vanilla extract. Mix in flour mixture and milk until just incorporated.
Shape into 40 balls and place each into an ungreased mini muffin pan. Bake in preheated oven until cookies are golden brown, about 8 minutes. Remove from oven and immediately press a mini peanut butter cup into the center of each cookie. Cool and carefully remove from pan.