Preheat the oven to 350 degrees F.
Drain 1 can of peaches; reserve the syrup from the other. Place the butter in a 9- by 12-inch ovenproof baking dish. Heat the butter on the stove or in the oven until it's melted. In a medium bowl, mix the flour and sugar. Stir in the milk and the reserved syrup. Pour the batter over the melted butter in the baking dish. Arrange the peaches over the batter. Bake for 1 hour. The cobbler is done when the batter rises around the peaches and the crust is thick and golden brown. Serve warm with fresh whipped cream
Chill a large metal mixing bowl and the wire beater attachment in the freezer for about 20 minutes. Pour the chilled cream and sugar into the cold mixing bowl and beat until it forms soft peaks, about 5 minutes. The mixture should hold its shape when dropped from a spoon. Don't overbeat or you'll have sweetened butter!
If you don't have self-rising flour, substitute 1 cup all-purpose flour mixed with 1 1/2 teaspoons baking powder and 1/8 teaspoon salt
Recipe adapted from Georgia Cooking in an Oklahoma Kitchen by Trisha Yearwood (c) Clarkson Potter 2008