Begin by gathering all of the ingredients. Peel, core, and thinly slice the apples, then set them aside. Preheat your oven to 425°F (220°C).

In a saucepan over medium heat, melt the butter. Stir in the flour to create a paste, cooking it until aromatic, about 1 to 2 minutes. Next, add both the white and brown sugars along with the water, and bring the mixture to a boil. Lower the heat and let it simmer for 3 to 5 minutes before removing it from the heat.

Press one pie pastry into the bottom and up the sides of a 9-inch pie pan. Roll out the second pastry, ensuring it is large enough to overhang the edges of the pie pan by about ½ inch. Slice this pastry into eight 1-inch strips.

Fill the prepared pie crust with the sliced apples, mounding them slightly in the center. Arrange four of the pastry strips vertically over the apples, spacing them evenly and using longer strips in the middle and shorter ones at the sides.

To create a lattice pattern, fold back the first and third strips almost entirely off the pie. Place one of the unused strips horizontally over the second and fourth vertical strips, then unfold the first and third strips to their original positions.

Next, fold back the second and fourth vertical strips. Lay another unused strip across the pie horizontally, then return the folded strips back to their places.

Repeat this process to finish weaving the last two strips of dough. Trim any excess from the edges and pinch to seal the crust neatly.

Slowly pour the sugar-butter mixture over the lattice crust, ensuring it seeps through to cover the apples. Lightly brush some of the mixture onto the pastry strips, avoiding any runoff over the edges.

Place the pie in the oven and bake for 15 minutes. Then, reduce the oven temperature to 350°F (175°C) and continue baking for an additional 35 to 45 minutes, or until the apples are tender.