Preheat and prep the dish: Heat your oven to 350°F (175°C).
Grease a 9x13-inch baking dish or a similar 3-quart baking dish.
Peel and slice the apples: Peel, core, and slice the apples into 1/4-inch thick pieces. Aim for even slices so they cook at the same rate.
Season the apples: In a large bowl, toss the apples with 1/3 cup granulated sugar, 1/4 cup brown sugar, 1 tablespoon lemon juice, 1 teaspoon cinnamon, a pinch of nutmeg (optional), and 1 tablespoon cornstarch. Spread evenly in the baking dish.
Make the cobbler batter: In another bowl, whisk 1 cup flour, 3/4 cup granulated sugar, 1 1/2 teaspoons baking powder, and 1/4 teaspoon salt.
Add 1/2 cup milk, 1 teaspoon vanilla, and 6 tablespoons melted butter. Stir just until combined. The batter will be thick and spoonable.
Top the apples: Drop spoonfuls of batter over the apples, leaving small gaps.
It doesn’t need to cover perfectly; it will spread as it bakes.
Optional sugar sprinkle: For a lightly crisp lid, sprinkle 1–2 teaspoons granulated sugar (or coarse sugar) over the batter.
Bake: Place the dish on the center rack and bake 40–50 minutes, until the topping is golden and a toothpick inserted into the topping comes out clean. The apple filling should be bubbling around the edges.
Rest and serve: Let the cobbler rest for 10–15 minutes. This helps the juices thicken.
Serve warm with ice cream or whipped cream.