In a large bowl, combine the butter, sugar, eggs and vanilla. In a small bowl, combine the flour, cocoa, baking powder and salt; set aside 1/4 cup. Stir remaining dry ingredients into the egg mixture until well combined. Toss Snickers pieces with reserved flour mixture; stir into batter.
Transfer to a greased 13x9-in. baking pan. Sprinkle with milk chocolate candy bar pieces. Bake at 350° for 30-35 minutes or until a toothpick inserted in the center comes out clean (do not overbake). Cool on a wire rack. Chill before cutting.