Step 1: To easily peel peaches, blanch them by dropping them into boiling water for 30-60 seconds, then immediately transferring to an ice bath. The skins should slip off easily.
Step 2: Halve the blanched peaches, remove pits, and slice into 1/2-inch thick wedges. You should have about 8 cups of sliced peaches.
Step 3: In a large bowl, combine the sliced peaches with 1/2 cup granulated sugar, 2 tablespoons cornstarch (or flour), 1 teaspoon vanilla extract, 1/2 teaspoon cinnamon, and 1/4 teaspoon nutmeg. Toss gently to coat and set aside.
Step 4: Preheat your oven to 375°F (190°C). Lightly butter a 9×13-inch baking dish or a 9-inch round cast iron skillet.
Step 5: In a separate medium bowl, whisk together 1 1/2 cups all-purpose flour, 1/2 cup granulated sugar, 1 tablespoon baking powder, and 1/2 teaspoon salt.
Step 6: Add the cold, cubed butter to the dry ingredients. Using a pastry blender, two knives, or your fingertips, cut the butter into the flour mixture until it resembles coarse crumbs with some pea-sized pieces of butter remaining.
Step 7: Gradually stir in 1/2 cup milk until just combined. Be careful not to overmix; the dough will be shaggy.
Step 8: Pour the prepared peach mixture evenly into the buttered baking dish.
Step 9: Drop spoonfuls of the cobbler topping over the peach filling. You can arrange them somewhat evenly or simply dollop them as desired. Sprinkle the top with the remaining 1 tablespoon of granulated sugar.
Step 10: Bake for 35-45 minutes, or until the topping is golden brown and the peach filling is bubbling thickly around the edges. If the topping browns too quickly, loosely tent the dish with foil.
Step 11: Remove the cobbler from the oven and let it cool for at least 15-20 minutes before serving. This allows the juices to set and thicken for the perfect consistency. Serve warm with vanilla ice cream or whipped cream.