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, sugar, and cinnamon. 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 with whipped cream or ice cream.