Gather the ingredients. Heat the oven to 425 degrees F (220 degrees C). Peel and core the apples, then cut them into thin slices and set them aside.
Place the butter in a saucepan over medium heat and melt it. Stir in the flour until a paste forms, then cook for 1 to 2 minutes, until fragrant. Stir in the white sugar, brown sugar, and water and bring the mixture to a boil. Turn the heat to low and simmer for 3 to 5 minutes, then take the saucepan off the heat.
Fit one pastry crust into the bottom and along the sides of a 9-inch pie pan. Roll out the second pastry so that it extends roughly 1/2 inch beyond the edge of the pie. Slice this pastry into eight 1-inch strips.
Fill the bottom crust with the sliced apples, arranging them so they rise slightly higher in the center. Position four pastry strips vertically across the apples at even intervals. Place the longer strips toward the middle and the shorter ones near the sides.
Begin weaving the lattice by folding the first and third vertical strips all the way back, nearly to the edge of the pie. Place one unused strip crosswise over the second and fourth strips. Return the first and third strips to their original positions.
Fold back the second and fourth vertical strips. Position another unused strip crosswise over the top, then return the second and fourth strips to place. Continue the same weaving process with the final two pastry strips. Trim or fold away any extra dough around the perimeter as needed, then pinch the edges to seal them.
Slowly pour the warm sugar-butter mixture over the lattice, allowing it to work its way through the openings and onto the sliced apples. Lightly coat the lattice itself as well, taking care to keep the mixture from spilling over the sides.
Bake at 425 degrees F (220 degrees C) for 15 minutes. Lower the oven temperature to 350 degrees F (175 degrees C) and bake for another 35 to 45 minutes, or until the apples are tender.
Serve and enjoy.