Preheat the oven to 425 degrees F (220 degrees C). Peel and core apples, then thinly slice. Set aside.

Melt butter in a saucepan over medium heat. Add flour and stir to form a paste; cook until fragrant, about 1 to 2 minutes. Add both sugars and water; bring to a boil. Reduce the heat to low and simmer for 3 to 5 minutes. Remove from the heat.

Press one pastry into the bottom and up the sides of a 9-inch pie pan. Roll out remaining pastry so it will overhang the pie by about 1/2 inch. Cut pastry into eight 1-inch strips.

Place sliced apples into the bottom crust, forming a slight mound. Lay four pastry strips vertically and evenly spaced over apples, using longer strips in the center and shorter strips at the edges.

Fold the first and third strips back, lay one unused strip perpendicularly. Repeat weaving steps for the lattice crust. Pinch to secure the edges.

Slowly and gently pour sugar-butter mixture over lattice crust, making sure it seeps into apples. Brush some onto lattice.

Bake in the preheated oven for 15 minutes. Reduce the temperature to 350 degrees F (175 degrees C) and continue baking until apples are soft, 35 to 45 minutes.