Preheat oven to 350 degrees F and place rack in the center of the oven. Butter, or spray with a non stick vegetable spray, 48 miniature muffins tins.
In a bowl, whisk together the flour, baking soda, and salt.
In the bowl of your electric mixer (or with a hand mixer), cream the butter. Add the sugars and beat until light and fluffy (about 2 - 3 minutes). Add the eggs, one at a time, beating well after each addition. Beat in the vanilla extract. Add the flour mixture and beat just until incorporated. Fill each miniature muffin cup with about one tablespoon of batter.
Bake the cookies for about 8 minutes, or until the cookies are lightly browned around the edges but still soft in the center. (Note: While the cookies are baking remove the foil wraps and paper liners from each peanut butter cup.) Remove the cookies from the oven, and gently press one miniature peanut butter cup into the center of each cookie.
The peanut butter cup should be even with the top of the batter. Return the cookies to the oven and bake an additional 3 minutes or until cookies are golden brown. Remove from oven and cool completely (about two hours) on a wire rack before removing the cookies from the pan. These can be stored for several days at room temperature or in the refrigerator, or they can be frozen.