Move an oven rack to the second-lowest position for better bottom-crust baking.

Tear off a piece of foil slightly larger than your pie dish and place it on the lowest rack to catch drips while still allowing airflow.

Preheat oven to 425°F.

Peel, core, and slice apples. Aim for even slices so they soften at the same speed.

On a lightly floured surface, roll one pie crust into about a 12-inch circle and fit it into a 9-inch pie dish, leaving a little overhang.

In a large bowl, toss apple slices with 2 tablespoons flour.

Spoon apples into the crust, mounding slightly in the center.

Roll the second crust into a 12-inch circle, then cut into strips about 1 to 1½ inches wide.

Lay half the strips across the pie in one direction, spacing them slightly apart.

Weave the remaining strips the other way to create a lattice pattern.

Trim excess strip ends, pinch the lattice and bottom crust together to seal, then crimp the edges.

In a saucepan over medium heat, melt the butter.

Whisk in the remaining 3 tablespoons flour to form a smooth paste.

Add water, white sugar, and brown sugar. Bring to a gentle boil, then reduce heat and simmer briefly until slightly thickened.

Slowly pour the sauce over the lattice so it flows into the openings and coats the apples.

Bake at 425°F for 15 minutes.

Reduce temperature to 350°F and bake for about 45 minutes more, until the crust is golden and the filling is bubbling.

If crust edges start browning too quickly, cover them with foil.

Transfer the pie to a wire rack.

Cool for about 2 hours before slicing.

Serve with vanilla ice cream, whipped cream, or extra sauce from the pan.