Preheat oven to 350°.
Place 2 teaspoons melted butter in the bottom of a 9-inch round cake pan; sprinkle with brown sugar and lemon rind. Top with blackberries; set aside.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, and salt in a small bowl.
Beat granulated sugar and 2 tablespoons butter in a large bowl at medium speed of a mixer until well-blended. Add the egg and vanilla; beat well. Add flour mixture to egg mixture alternately with milk, beginning and ending with flour mixture; mix after each addition. Spoon batter over blackberries.
Bake at 350° for 40 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 5 minutes on a wire rack. Loosen edges of cake with a knife. Place a plate upside down on top of cake pan; invert onto plate.