Preheat oven to 350°. Prepare brownie batter according to package directions; stir in peanut butter chips. Bake in a greased 13x9-in. baking pan 20-25 minutes. Cool on a wire rack; cut into 3/4-in. pieces.
Cut peanut butter cups in half; set aside 1/3 cup for garnish.
Whisk milk and pudding mixes for 2 minutes. Mix in peanut butter and vanilla. Fold in 1-1/2 cartons whipped topping.
Place a third of the brownies in a 5-qt. glass bowl; top with a third of the remaining peanut butter cups. Spoon a third of the pudding mixture over the top. Repeat layers twice. Cover with remaining whipped topping; garnish with reserved peanut butter cups. Refrigerate.