Prepare brownie batter according to package directions; stir in peanut butter chips. Bake in a greased 13-in. x 9-in. baking pan at 350° for 20-25 minutes or until a toothpick inserted near the center comes out with moist crumbs (do not overbake). Cool on a wire rack; cut into 3/4-in. pieces.
Cut peanut butter cups in half; set aside 1/3 cup for garnish. In a large bowl, whisk milk and pudding mixes for 2 minutes (mixture will be thick). Add peanut butter and vanilla; mix well. 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 until chilled.