In a large mixing bowl, using an electric mixer, cream the butter, peanut butter, granulated sugar, and light brown sugar until light and fluffy.
Beat in the eggs and vanilla.
In a separate bowl whisk together the flour, baking soda and salt; gradually add the flour mixture to the creamed mixture and mix until well combined. Stir in the chopped peanut butter cups.
Drop by rounded tablespoonfuls 2 inches apart onto ungreased cookie sheets.
Bake for 10 to 12 minutes or until edges are lightly browned.
Remove from oven and cool for 2 minutes; transfer to wire racks to cool completely.