Preheat oven to 350° F.
Place the sliced apples in a large mixing bowl. Sprinkle the remaining filling ingredients over the apples: ¼ cup brown sugar, ¼ cup granulated sugar, 2 tablespoons flour, 1 teaspoon cinnamon, ¼ teaspoon nutmeg and ¼ teaspoon salt. Stir to combine and set aside.
To make the cobbler dough, in a medium bowl, combine the 1 ¼ cups flour, ¼ cup granulated sugar, 1 ½ teaspoons baking powder, ½ teaspoon cinnamon and ½ teaspoon salt. Whisk until well combined.
Add the cold butter cubes and use your fingers or a pastry blender to work the butter into the flour mixture until the largest pieces of butter are the size of small peas.
Add the milk and use a fork to mix the dough just until it comes together.
Stir the apple mixture once more to make sure that everything is well combined and then pour it into a lightly greased 8x8 or 9x9-inch baking dish. Spread the apples out into an even layer.
Use a spoon to scoop portions of the biscuit dough and place on top of the apples (you should get about 12 spoonfuls of dough total). The topping should mostly cover the apples, with just a few apples peeking through. Sprinkle the 1 teaspoon of sugar over the top of the dough.
Bake for 45-50 minutes, until the filling is very bubbly, the apples are soft, the topping is golden brown on top and the undersides of the biscuits are cooked through. Let cool for at least 10 minutes before serving.