Preheat the oven to 375°F (190°C).
Prepare the apple filling by combining sliced apples, granulated sugar, lemon juice, cinnamon, and nutmeg in a large mixing bowl.
Transfer the apple mixture to a greased 9x13 inch baking dish, spreading it evenly.
In another bowl, mix together flour, brown sugar, baking powder, and salt.
Stir in the melted butter and milk until just combined, creating a thick batter.
Drop spoonfuls of the batter over the apple filling in the baking dish, covering as much as possible.
Bake for 35-40 minutes or until the topping is golden brown and the apples are bubbly.
Let the cobbler cool for about 15 minutes before serving warm, ideally with a scoop of ice cream or whipped cream.