Preheat the oven to 350 degrees F (175 degrees C).
Mix peaches with 1 cup sugar in a bowl until coated; set aside. Combine flour, milk, 3/4 cup sugar, baking powder, and salt in another bowl.
Pour butter into a 9x13-inch glass baking dish. Pour flour mixture over the melted butter. Spoon peaches over the flour, sprinkle generously with cinnamon, and sprinkle with shredded cheese.
Bake in the preheated oven until filling is bubbly and cheese is golden brown, about 1 hour.