In a medium bowl, cream the butter, white sugar, brown sugar, and peanut butter together. Stir in the egg and vanilla. Sift together the flour, baking soda and salt; stir into the creamed mixture.
Drop by tablespoonfuls into the cups of a muffin tin. Cups should be about 1/4 full. Bake for 8 to 10 minutes, until lightly browned. Remove from oven and immediately press a peanut butter cup into the center of each cookie. Allow the cookies to cool completely before removing from their pan.