Using an electric mixer, beat butter and peanut butter on high speed until combined, about 30 seconds.
Add both sugars and beat again until combined, scraping sides as needed. Add the egg and vanilla and briefly beat mixture.
In a separate bowl, combine baking soda, baking powder, and flour. Slowly add flour mixture to wet mixture and beat until mixed. Chill dough for 30 minutes.
To assemble bars, evenly press half of the dough in an ungreased 9x9 baking pan. Arrange the Reese's peanut butter cups on top of the dough, about 3.5 Reese's per row. Press the remaining peanut butter cookie dough over the top of the Reese's.
Sprinkle the chopped peanuts over the top of the bars. Lightly press into the top of the dough.
Bake for 30-35 minutes until light brown. Allow to cool slightly.
Prepare candy melts per package directions. Drizzle melted chocolate over the top of the bars. Cut into 16 servings.