Place 4 tablespoons of butter in a 9x13-inch baking dish and place the baking dish inside the oven while you preheat it to 350 F. Once melted, use it to grease the sides of the dish and leave the rest on the bottom.
Heat the canned peaches (with juice) in a saucepan with 1 cup of sugar and ½ cup of water over medium heat. Once the peaches are simmering, dissolve the cornstarch in the remaining water and add it to the saucepan.
Simmer this mixture until thick, about 3 minutes. Remove from heat and set aside.
Make the batter by whisking together the flour, vanilla, 1 ½ cups of sugar, and milk.
Spoon the peaches and their thick juice into the baking dish with the melted butter (do not mix) and spread the batter over the peaches. Don’t worry if it doesn’t fully cover the peaches.
Make cinnamon sugar by mixing the remaining sugar with the cinnamon, sprinkle it evenly over the batter, and bake for 30 minutes or until slightly golden brown.