Preheat the oven to 350 degrees. Put the butter into a 9 x 13 inch Pyrex style baking pan. Place the pan in the preheated oven to melt the butter.
In a medium sized mixing bowl, stir together the flour, sugar, baking powder and salt. Stir in the milk and beaten egg until all of the ingredients are well combined. Remove the casserole from the oven and pour the flour mixture evenly over the melted butter. DO NOT MIX.
In the same bowl you used for the flour mixture, toss together the peaches,sugar, cinnamon and nutmeg. Spoon the peach mixture evenly over the batter in the casserole. DO NOT STIR. Bake in the preheated oven for about 35 to 45 minutes, or until the batter rises to the top and is golden brown.