Preheat oven to 350 degrees. Use parchment paper or a silpat mat to line a baking sheet.
Cream the butter, peanut butter, and sugars in a stand mixer until light and fluffy (about 2-3 minutes). Scrape the sides of the bowl to make sure all ingredients are blended.
Add in the egg and vanilla and beat until combined.
Add in flour, baking soda, corn starch, salt and baking powder. Mix until all combined.
Gently stir in the chopped up Reese's peanut butter cups.
Scoop out about 1 tablespoon (or use a 1 tbsp cookie scoop) and roll into a dough ball and slightly flatten into a 1" high disc. Place dough discs on a wax covered plate and freeze for 15 minutes.
Remove the dough from the freezer and bake at 350 degrees on the prepared baking sheet for 9 minutes.
Add the peanut butter chips and oil to a microwave safe bowl and microwave in 30 second increments until melted.
Top each slightly cooled cookie with a spoonful (about 1 teaspoon) of the melt peanut butter and spread carefully. Top with a few pieces of chopped up Reese's peanut butter cups.