Place the butter into a 9-inch square pan and bake for 2 to 3 minutes or until the butter is completely melted. Remove from the oven and set aside.
In a medium bowl, whisk together the flour, white sugar, and milk. Pour the mixture directly over the melted butter but do not stir!
In a small saucepan combine the peaches, brown sugar, lemon juice, cornstarch, cinnamon, and nutmeg. Stir until combined. Bring to just a boil over medium heat stirring constantly. Pour the peach mixture over the batter in the pan -making sure to evenly distribute the peaches.
Bake 40 to 45 minutes or until golden brown. Serve warm with your favorite ice cream.
As a substitute for self-rising flour, place 3/4 teaspoon baking powder and 1/4 teaspoon salt in a 1/2 cup measuring cup. Add all-purpose flour to measure 1/2 cup.
Decrease the amount of brown sugar according to taste. For riper, sweeter peaches you may not need a full 1/2 cup.