Preheat and Prepare Apples: Preheat the oven to 425°F (220°C). Peel, core, and thinly slice the apples.
Make Caramel Sauce: Melt butter in a saucepan over medium heat. Stir in flour to form a paste and cook for 1-2 minutes. Add white sugar, brown sugar, and water. Bring to a boil, then simmer for 3-5 minutes.
Prepare Pie Crust: Line a 9-inch pie pan with one pastry. Roll out the second pastry and cut into eight 1-inch strips.
Assemble Pie: Fill the bottom crust with sliced apples, forming a mound. Arrange four pastry strips vertically and weave the remaining strips horizontally to create a lattice.
Add Caramel: Slowly pour the sugar-butter mixture over the lattice crust and apples, brushing some onto the pastry.
Bake: Bake at 425°F for 15 minutes. Lower the temperature to 350°F (175°C) and bake for another 35-45 minutes until the apples are tender.
Cool and Serve: Allow the pie to cool before slicing and serving.