Preheat oven to 350°F. Mash raspberries slightly with a potato masher and set aside.
In a bowl combine flour, 1 tablespoon cocoa powder, and baking powder; set aside. In a medium mixing bowl beat butter with an electric mixer on medium speed for 30 seconds. Add 1/2 cup brown sugar and the vanilla; beat until well combined. Alternately add flour mixture and milk, beating until smooth after each addition.
Spread batter in a greased 2-quart square baking dish. Spoon raspberries over batter. Combine remaining 1/3 cup brown sugar and 2 tablespoons cocoa powder; sprinkle evenly over batter.
Bake about 40 minutes or until wooden toothpick, inserted about 1/2 inch into cake portion, comes out clean. Cool about 1 hour on a wire rack. Serve warm. Makes 6 servings.