Preheat oven to 375 degrees F (190 degrees C). Pour butter into an 8-inch square baking dish.

Combine peaches and 3/4 cup sugar together in a bowl. Whisk flour, remaining sugar, baking powder, salt, and nutmeg together in a bowl; stir in milk just until batter is combined. Pour batter over butter and top with peaches.

Bake in the preheated oven until cobbler is golden brown, 45 to 50 minutes.