Pre-heat oven to 350℉. Peel, core, and slice apples into thin, uniform slices, about ¼ inch thick. As you are slicing the apples, toss them in a bowl with apple juice (enough to cover the apple slices) to prevent browning.
Once the apples are all sliced, drain the apples in a colander placed on top of a bowl. Save the apple juice.
In a large sauce pan, whisk the dry ingredients together - the sugars, cornstarch, cinnamon, salt, and nutmeg.
Add 1 ½ cups apple juice (use the apple juice used to cover the apple slices) to the dry ingredients. The mixture will be thick, but as the sugars melt, it will thin out.
Bring to a boil, stirring with a whisk until it reaches the consistency of a thick glaze. Whisk in a little more apple juice if it becomes too thick.
Stir drained apple slices into the glaze.
Cover and reduce heat to medium-low. Cook until the apples just start to soften and become limp. Stir every couple of minutes. This should take about 5-7 minutes.
Pour hot apple filling into the graham cracker crust. Do not overfill the pie crust. Leave space for the crumb topping.