Preheat the oven to 350 degrees F. Butter a 13 by 9 by 2-inch baking dish.
Using an electric mixer, combine the butter and sugar in a large mixing bowl; beat at medium speed until creamy. Add the eggs, 1 at a time, beating well after each addition. Stir in the vanilla and mix well.
In a separate bowl, combine the flour, cocoa, and baking powder. Gradually stir the flour mixture into the butter mixture. Spoon it into the baking dish and bake for 35 minutes. Let cool completely, then cut into 16 squares.
Heat a grill or grill pan to medium heat.
Spread the marshmallow creme evenly over 8 brownies, and top with the chocolate covered peanut butter cups. Top with the remaining brownies. Wrap each brownie sandwich in heavy-duty aluminum foil. Grill for 4 minutes, turning once. Unwrap and serve immediately.
Recipe courtesy of Paula Deen (GC, pg. 127)