Preheat oven to 375°F (190°C) with a rack in the middle position. Lightly grease a 9-inch square baking dish with butter or cooking spray, coating the corners and sides.
Peel, core, and slice 6 medium apples into 1/4-inch thick pieces (about 6 cups). Toss immediately with 2 tablespoons lemon juice to prevent browning.
In a large bowl, combine sliced apples, 3/4 cup sugar, 2 tablespoons flour, 1 teaspoon cinnamon, and 1/4 teaspoon nutmeg. Stir gently until evenly coated and let sit 5 minutes.
Transfer the apple filling to the prepared baking dish and spread into an even layer.
In a medium bowl, whisk together 1 cup flour, 1/4 cup sugar, 1 1/2 teaspoons baking powder, and 1/2 teaspoon salt. Cut in 1/4 cup cold cubed butter with a pastry cutter or fork until mixture resembles coarse crumbs with pea-sized butter pieces.
Pour in 1/2 cup whole milk and stir just until a dough forms, being careful not to overmix. Add more milk one teaspoon at a time if dough feels too dry.
Drop spoonfuls of dough evenly over the apple filling, leaving some gaps between spoonfuls so steam can escape while baking.
Bake for 40 to 45 minutes, until the topping is deep golden brown and filling bubbles thickly around the edges. Check at 35 minutes and loosely cover with foil if browning too quickly.
Let the cobbler cool for 10 minutes before serving so the juices can set. Serve warm in bowls, topped with ice cream or whipped cream if desired.