Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.
Cream butter, peanut butter, and sugars together for 2–3 minutes until light and fluffy.
Add egg, egg yolk, and vanilla and mix until smooth.
Whisk dry ingredients (flour, cornstarch, baking soda, baking powder, and salt) in a separate bowl, then mix into the dough just until combined.
Fold in chopped peanut butter cups evenly.
Scoop large dough balls (about ¼ cup each), roll smooth, and gently flatten into thick discs.
Bake for 11–13 minutes until edges are set and centers remain soft. Let cool on the pan for 10–15 minutes, then transfer to cool completely.
Melt peanut butter chips in short microwave bursts, stirring until smooth. Add a small amount of oil or milk if needed for a spreadable consistency.
Spread a thick layer of melted peanut butter on each cooled cookie.
Drizzle melted milk chocolate over the top.
Sprinkle chopped peanut butter cups and gently press to set.