In a medium bowl, cream together the brown sugar, white sugar and butter. Stir in the peanut butter, then the egg and vanilla. Sift together the flour, baking soda and salt, stir into the peanut butter mixture until the dough comes together. Shape into 1 inch balls and press them into the cups of an unprepared mini muffin pan.
Bake for 8 to 10 minutes in the preheated oven. As soon as the cookies come out of the oven, press a mini chocolate covered peanut butter cup down into the center of each cookie until only the top is showing. Allow the cookies to cool completely before removing from their pans.