Preheat the oven to 350°F. Grease a mini muffin tin with cooking spray.
In a medium bowl, whisk together the flour, baking soda and salt. Set it aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, sugar and brown sugar until light and fluffy, about 2 minutes. Add the eggs one at a time, beating between each addition, then beat in the peanut butter and vanilla extract.
Add the flour mixture to the stand mixer, beating just until combined.
Using a small ice cream scoop (or two spoons), scoop heaping 1-tablespoon portions into the muffin tin cups.
Bake the cookies for 18-22 minutes.
Remove the cookies from the oven, then immediately push a mini peanut butter cup into the center of each cookie. Let the cookies cool completely in the pan then serve. (See Kelly’s Note.)