Preheat your oven to 375°F (190°C) and lightly grease a 9-inch baking dish or deep-dish pie plate.
Prepare the apple filling by combining the sliced apples, sugar, gluten-free flour, lemon juice, cinnamon, nutmeg, and salt in a large bowl. Toss until all apple slices are evenly coated with the mixture.
Transfer the apple mixture to your prepared baking dish, arranging it evenly. The dish will look quite full, but the apples will cook down during baking.
Make the cobbler topping by whisking together the gluten-free flour, granulated sugar, brown sugar, baking powder, cinnamon, and salt in a medium bowl.
Cut in the cold butter using a pastry cutter or fork until the mixture resembles coarse crumbs with some pea-sized pieces remaining. This texture is crucial for a tender topping.
Whisk together the milk, egg, and vanilla in a small bowl, then pour into the flour-butter mixture. Stir just until combined – the batter will be thick and slightly lumpy.
Drop spoonfuls of the topping over the apples, covering most of the surface but allowing some gaps for the filling to bubble through during baking.
Bake for 40-45 minutes until the topping is golden brown and the filling is bubbling around the edges. If the topping browns too quickly, loosely cover with foil.
Allow the cobbler to cool for at least 15 minutes before serving to let the filling set slightly and avoid burning mouths!