Preheat the oven: Set the oven to 350°F and lightly butter a 9x13-inch baking dish so the filling doesn't stick to the edges.
Prep the apples: Peel, core, and slice the apples into even half-inch wedges. Toss them with lemon juice right away to keep them from browning.
Season the filling: Add granulated sugar, brown sugar, cinnamon, and nutmeg to the apples and toss until every slice looks glossy and coated.
Spread the apples: Pour the apple mixture into the prepared baking dish and spread it into an even layer so it cooks at the same rate.
Mix the dry topping: In a separate bowl, whisk together flour, sugar, baking powder, and salt until evenly combined.
Add milk and butter: Stir in the milk and melted butter until just combined into a thick, pourable batter. Avoid overmixing or the topping can turn dense.
Pour over the apples: Pour the batter evenly over the apple layer, letting some gaps show so steam can escape while baking.
Bake until golden: Bake for 40 to 45 minutes, until the topping is deep golden brown and the filling bubbles up around the edges.
Rest before serving: Let the cobbler cool for 10 to 15 minutes so the juices thicken slightly and the topping finishes setting.