Press pie crust dough into the bottom of a 9-inch pie pan. Prick sides and bottom of dough with a fork.
Bake in the preheated oven until lightly browned, 10 to 12 minutes. Cool completely.
Beat cream cheese, peanut butter, and confectioners' sugar together in a bowl until smooth. Fold 1 cup whipped topping into cream cheese mixture. Spread into cooled pie crust. Chill in refrigerator until set, 1 hour.
Mix vanilla pudding mix and chocolate pudding mix with milk in a bowl until pudding starts to set up, about 2 minutes; spread over cream cheese mixture in pie crust. Spread 1 cup whipped topping over the pie. Sprinkle with shaved chocolate and peanuts. Chill in refrigerator before serving, about 1 hour.
