Preheat the oven: Set to 350°F (175°C). Place a 9x13-inch baking dish (or a deep 10-inch skillet) in the oven with 1/2 cup (1 stick) of butter to melt. Keep an eye on it so it doesn’t brown too much.

Prep the peaches: Drain the canned peaches, reserving about 1/2 cup of the juice or syrup. If the slices are very large, cut them in half. Toss peaches with 1–3 tablespoons sugar (to taste), 1/2 teaspoon cinnamon, 1 teaspoon vanilla, and 1 teaspoon lemon juice. If you prefer a thicker filling, stir 1 teaspoon cornstarch into the reserved juice until smooth, then add to the peaches.

Make the batter: In a bowl, whisk 1 cup all-purpose flour, 1 cup sugar, 2 teaspoons baking powder, and 1/4 teaspoon salt. Add 1 cup milk and stir just until smooth. Don’t overmix.

Build the cobbler: Carefully remove the hot baking dish from the oven. Swirl the melted butter to coat the bottom. Pour the batter evenly over the butter—do not stir. Spoon the peaches and their juices over the batter. Again, don’t stir. The batter will rise up around the fruit as it bakes.

Bake: Return to the oven and bake for 40–50 minutes, until the top is golden and the edges are crisp. The center should be set and bubbling.

Rest and serve: Let the cobbler cool for at least 10–15 minutes so the juices thicken slightly. Serve warm with ice cream or whipped cream.