Preheat oven to 375 degrees F.
Cream butter, peanut butter, sugar and brown sugar. Beat in egg and vanilla.
Sift flour, baking soda and salt. Blend into creamed mixture. Shape into 1-inch balls and place in ungreased 1-1/2-inch muffin tins.
Bake at 375 degrees for 8 to 10 minutes or until lightly browned. Without removing from the pan, press a peanut butter cup into the center of each. Cool about 10 minutes before removing from tins.