Place 1/4 cup butter in an 8x8x2-inch baking pan. Warm in a 350 degrees F oven about 5 minutes or until butter is melted. (Be sure to watch carefully to avoid overbrowning the butter). Remove pan from oven. Add brown sugar, stirring until sugar is completely moistened. Spread sugar mixture evenly in pan. Arrange peach slices evenly over brown sugar mixture. Set aside.
In a medium bowl, combine the flour, baking powder and salt; set aside. In a large bowl, beat 1/2 cup butter with an electric mixer on medium to high speed for 30 seconds. Beat in granulated sugar until well combined. Add egg and vanilla, beating until combined. Alternately add the flour mixture and milk to beaten butter mixture, beating on low speed after each addition just until combined. Spread batter evenly over the peaches in the pan.
Bake for 45 to 50 minutes or until a wooden toothpick inserted near the center comes out clean. Cool in pan on wire rack for 5 minutes. Loosen cake from sides of pan; invert onto a large serving plate. Cool for 10 to 15 minutes more. Serve warm. Makes 8 servings.