Preheat oven to 350F. Lightly grease 2 mini-muffin pans (24 cup each), with butter or nonstick cooking spray.
In a medium bowl, sift together the flour, baking soda, and salt. In a large mixing bowl, cream together butter and sugar until light and fluffy, 3 to 5 minutes. Add eggs one at a time, mixing thoroughly between additions. Add vanilla extract and stir to combine. Add dry ingredients to butter mixture and mix until combined. Scoop 1 tablespoon of cookie dough into each cup of prepared mini-muffin pan.
Bake 8 minutes in preheated oven, or until lightly browned. Remove cookies from oven. Working quickly, press one miniature peanut butter cup into the center of each cookie. Press the peanut butter cup down until the edge of the cookie and peanut butter cup are even. Return the cookies to the oven and bake 3 additional minutes or until the cookies are golden brown. Remove from oven and cool in pan on wire racks until room temperature. Makes 48 cookies.