Cut butter into approximately 6 slices and lay them in the bottom of a deep 11x7 inch baking dish or a 9x13 inch baking dish.
Place the dish in the oven and set to preheat to 350 degrees F. If the oven finishes preheating before you have the remaining ingredients prepared you can remove the dish from the oven until you are ready to use.
While the oven preheats make your batter. Combine all-purpose flour, baking powder, salt, sugar, and brown sugar in a large bowl and whisk together until well combined. Make sure there are no chunks of brown sugar.
Slowly pour the milk into the dry ingredients whisking as you go to keep it from clumping. Add the vanilla extract and whisk until the batter is smooth.
In a small bowl or ramekin combine the water and cornstarch and whisk together with a fork or spoon until well blended. This is called a slurry.
Pour the peaches along with their juice into a separate large bowl and add the brown sugar, granulated sugar, and cinnamon. Pour in the cornstarch slurry into the peaches and stir everything together.
Pour the batter into the hot baking dish with the melted butter. Try to ensure you pour it so that it covers the whole bottom of the dish. DO NOT stir together with the butter.
Spoon the peaches and juice over the batter with a large spoon. Make sure to evenly distribute them. Do not stir together with the butter and batter.
Optional: Sprinkle a little extra cinnamon over the top of the cobbler.
Place the baking dish on a foil-lined baking sheet just in case the cobbler bubbles over as it bakes. Bake for 45 minutes or until golden brown on top and bubbling.
Once baked remove from oven and let rest for 20 minutes.
Serve warm.