Preheat the oven to 350 degrees. Line cookie sheets with parchment paper.
In a medium bowl whisk together the flour, baking soda, baking powder, and salt.
In a stand mixer, beat the butter and both sugars together until creamy. Add eggs, one at a time, and vanilla, and beat until combined.
Add the dry ingredients and mix on low until fully combined. Try not to overmix.
Stir in the chopped peanut butter cups.
Using a cookie scoop or spoon, roll the dough into balls (using about 2 tablespoons of dough per cookie) and set them about 2 inches apart on the cookie sheet.
Bake for 10-12 minutes until lightly golden. Allow to cool on the cookie sheet for about 5 minutes and then transfer them to a cooling rack. If you try to transfer too soon they will fall apart.