Preheat oven to 375F. Grease 2 24-tin mini muffin pans. Set aside.
In a large bowl, cream the butter and sugars together until well combined, about 3-4 minutes on medium.
Add the egg and vanilla. Mix until well combined, scraping the bowl as needed.
Add the peanut butter, and mix in until combined.
Add flour, baking soda, baking powder, and salt. Stir in until just combined.
Scoop 1 tablespoon cookie dough and place in prepared muffin tin cup.
Repeat with remaining dough.
Bake 7-10 minutes.
Remove from oven.
Gently press a mini peanut butter cup into each cookie.
Let the cookies cool to room temperature.
Remove from the muffin tin.
Notes
Butter: The butter should be warm enough to dent when pressed but shouldn't be soft and warm. Also, I use salted butter in this recipe.
Brown sugar: I use light brown sugar.
Peanut butter: I recommend using regular creamy peanut butter, not natural peanut butter in this recipe.
Flour: To properly measure the flour, weigh it (click on "metric" just above the ingredients for the weights). You can also stir or sift the flour to break it up. Then lightly spoon into the measuring cup and level. This helps to avoid packing in the flour.