Line a baking sheet with parchment paper and set aside.
Add fresh lemon juice to a large bowl. Peel and slice apples into ⅛-1/4 inch slices. As you slice the apples, add them to the bowl and make sure to cover the slices with the lemon juice to prevent the apples from turning brown.
Pour the apples into a large skillet and cook over medium heat. Add brown sugar, granulated sugar, flour, salt, cinnamon, nutmeg, and vanilla. Stir all ingredients together. Cover the apples for 20 or until the apples are tender. Stir the apples every 3-4 minutes.
Remove the apples from the heat and pour them in a single layer onto the prepared baking sheet. Cool in the refrigerator for 30-40 minutes.
Prepare your 9-inch pie plate with the pre-made dough. Pour the chilled filling into the prepared pie dish.
In a small bowl, mix together the milk and eggs. Brush the egg mixture around the edge of the pie crust ( This will seal the edges of the pie together). With your second piece of pie dough, roll it out and cup it into 1½ inch strips. Create a lattice pattern on top of the filling by weaving the pieces together. Crimp the edges of the pie together.
Place the whole pie back into the refrigerator for an additional 30 minutes to chill the pie crust. (This will help create a flaky crust)
Cover a baking sheet with a layer of tin foil and place it in the center of your oven. Preheat your oven to 425℉.
Remove the pie from the refrigerator and brush the top of the pie with the remaining egg mixture. Cover the crust with a pie crust cover or carefully wrap tin foil around the edges. Place the pie on the baking sheet and bake for 15 minutes.
Reduce the heat to 350℉ and bake for an additional 30 minutes. Remove the crust cover and bake for an additional 15-20 minutes or until the top of the pie turns a slight golden brown color.
Remove the pie from the oven and cool completely before serving.