Heat the oven to 375°F and butter a 9-by-13-inch baking dish.
Toss the apples with brown sugar, 2 tablespoons flour, lemon juice, cinnamon, nutmeg and 1/4 teaspoon salt; spread evenly in the dish.
Whisk the remaining flour with granulated sugar, baking powder and 1/2 teaspoon salt, then cut in the butter.
Stir in the milk, turn the soft dough onto a floured surface and pat it 3/4 inch thick.
Cut the dough into rough 3-inch squares and arrange them over the apples with small spaces between pieces.
Bake for 48 to 50 minutes until the apples are tender, the juices bubble and the topping is browned; rest 20 minutes.