Preheat oven to 350° F for glass or metal pans, and 325° F for dark or non-stick pans. Grease bottom of a 13- x 9-inch pan with cooking spray and set aside.
In a large bowl, with an electric mixer, beat brownie mix, 2 eggs, oil, 1 tablespoon vanilla, and water together on low speed until well blended (Please, do not over beat). Pour half of the batter into the prepared pan and spread evenly.
Beat mashed sweet potatoes, brown sugar, butter, 1/2 tablespoon vanilla, and granulated sugar at medium speed with an electric mixer until light and fluffy.
Add 2 eggs, one at a time, beating after each addition until just blended. Then, add the apple pie spice, baking powder, and flour to the sweet potato mixture, beating at low speed until just blended.
Spoon sweet potato mixture over brownie batter and spread even and gently; top with remaining brownie batter, spreading evenly.
Bake sweet potato-smores brownies for 30 to 35 minutes or until a wooden pick inserted in center comes out with a few moist crumbs. Remove sweet potato-smores brownies from oven to a wire rack and top with marshmallows.
Prepare Chocolate Frosting, and drizzle the hot frosting over sweet potato-smores brownies. Sprinkle Graham cracker crumbs on top and let cool completely.
Decorate sweet potato-smores brownies with small Graham cracker squares and enjoy!