Heat the oven. Preheat to 375°F (190°C). Place a 9x13-inch baking dish (or a 3-quart casserole) in the oven with the 1/2 cup butter to melt while it heats. Keep an eye on it so it doesn’t brown too much.

Prep the peaches. You’ll need about 5–6 cups sliced peaches. If using frozen, thaw slightly and pat dry. If using canned, drain well (reserve a little juice if you like). If using fresh, peel if you prefer, then slice.

Sweeten the fruit. In a bowl, toss peaches with 1/3–1/2 cup granulated sugar (adjust to taste), 1–2 tablespoons brown sugar (optional), 1 teaspoon lemon juice, and 1/2 teaspoon cinnamon. If your peaches are extra juicy, stir in 1 teaspoon cornstarch to help thicken the juices.

Make the batter. In another bowl, whisk together 1 cup flour, 1 cup granulated sugar, 2 teaspoons baking powder, and 1/4 teaspoon salt. Add 1 cup milk and 1 teaspoon vanilla; whisk just until smooth. The batter will be pourable.

Add butter to the dish. Remove the hot baking dish from the oven. Tilt it to coat the bottom evenly with the melted butter. Do not pour off excess; that butter helps the edges crisp.

Layer batter and peaches. Pour the batter into the dish over the butter. Do not stir. Spoon the peaches and their juices evenly on top. Again, don’t stir—the cobbler magic happens as it bakes.

Top with a sprinkle. For a bakery-style finish, mix 1 tablespoon sugar with a pinch of cinnamon and sprinkle over the top.

Bake. Bake for 40–50 minutes, until the top is golden and a toothpick inserted into the topping comes out mostly clean. The edges should be bubbling and crisp.

Rest and serve. Let it sit for 10–15 minutes so the juices settle. Serve warm with vanilla ice cream or whipped cream.