Preheat oven to 350 degrees F (175 degrees C). Place 1/2 cup butter in a casserole dish.

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Place casserole dish in the preheating oven until butter is melted. Remove.

Mix remaining 1/4 cup butter, peaches, 1/2 cup white sugar, brown sugar, cinnamon, nutmeg, and vanilla extract together in a bowl. Spread over melted butter in the casserole dish.

Mix remaining 1 cup white sugar, milk, flour, baking powder, and salt together in a bowl to make a smooth batter. Pour over peach mixture.

Bake in the preheated oven until golden brown, about 45 minutes. Let stand for 10 minutes before serving.