In a mixing bowl, combine butter, sugars, egg, peanut butter, and vanilla. Beat until smooth.
Combine flour, baking soda, and salt and add to creamed mixture. Cover dough and chill.
When cold enough to handle, roll into walnut size balls and place in greased or sprayed mini-muffin tins. Bake at 375° for 8-9 minutes or until lightly browned.
Remove from oven and immediately gently press an unwrapped peanut butter cup into the middle of each cookie. Cool in tin for 10 minutes.
Remove from tin and completely cool on wire rack. Store in cool place.