Preheat oven to 350°F and prepare a cookie sheet with parchment paper or non-stick spray. Chop the peanut butter cups into pieces, I usually chop one miniature cup into 6 pieces. Set aside.
In a medium-sized bowl, add the flour, salt, baking powder, and baking soda. Whisk together to combine and set aside.
In a separate, large bowl (or the bowl of a stand mixer), add the butter and sugars. Using a hand mixer (or the paddle attachment of a stand mixer) cream the butter and sugars together on high speed until light and fluffy, about 3 minutes.
Add the egg and vanilla to the butter and sugar, and again beat on high, this time for about 1-2 minutes, or until the egg is fully incorporated and the batter is very light and fluffy.
Add the dry ingredients to the wet ingredients, mixing together on low speed until almost all of the flour is incorporated. When there are just a few streaks of flour left, add half of the chopped peanut butter cups, and mix into the batter by hand with a rubber spatula, incorporating the last bit of flour and distributing the peanut butter cup pieces evenly throughout the batter.
Scoop the cookies and place them on a baking sheet. I used a 1 tablespoon scoop, and I was able to fit 15 cookies on my half sheet pan.
Bake in the preheated oven for 10-14 minutes, or until golden. When finished cooking, remove and immediately top the cookies with the remaining peanut butter cup pieces. Allow to cool before enjoying!