Preheat oven to 375 degrees F (190 degrees C). Sift together the flour, salt and baking soda; set aside.
Cream together the butter, sugar, peanut butter and brown sugar until fluffy. Beat in the egg, vanilla and milk. Add the flour mixture; mix well. Shape into 40 balls and place each into an ungreased mini muffin pan.
Bake at 375 degrees for about 8 minutes. Remove from oven and immediately press a mini peanut butter cup into each ball. Cool and carefully remove from pan.