Preheat the oven to 425°F.
In a large bowl, combine the sliced apples, lemon juice, 1/2 cup granulated sugar, brown sugar, cinnamon, and nutmeg. Toss until the apples are well coated. Set aside.
In another bowl, beat the softened cream cheese, remaining 1/2 cup granulated sugar, and vanilla extract until smooth and creamy.
Roll out one pie crust and fit it into a 9-inch pie pan. Spread the cream cheese mixture evenly over the bottom of the crust. Layer the apple mixture on top of the cream cheese.
Cover the pie with the second pie crust. Seal and crimp the edges, then cut a few slits in the top crust to allow steam to escape.
Brush the top crust with the beaten egg and sprinkle with 1 tablespoon of sugar.
Bake in the preheated oven for 15 minutes. Reduce the temperature to 350°F and continue baking for an additional 30-35 minutes, or until the apples are tender and the crust is golden brown.
Let the pie cool for at least 30 minutes before serving.