crust:
2 1/2 cup flour
1/2 tsp. salt
1 tbsp. sugar
1/2 cup + 2 tbsp. cold unsalted butter, cut into 1/2 inch cubes
1/2 cup shredded cheddar cheese (extra sharp cheddar works best)
6 to 8 tbsps. cold water

filling:
6 tbsps. unsalted butter
2 1/2 lbs. granny smith apples, sliced into 1/4 inch wedges
1/2 cup sugar
1/2 tsp. ground cinnamon
1/4 tsp. ground cloves
2 tbsps. lemon juice
2 tbsps. cornstarch

egg wash:
whisk together 1 egg and 2 tbsps. milk in s small bowl

Melt 3 tbsps of the butter in a large, heavy-bottom pan over medium
heat. Add the apples and saute for 3 to 4 minutes. Stir in the sugar,
cinnamon, cloves until combined.

Combine the lemon juice and cornstarch in a small bowl. Stir mixture
into the apple mixture and remove the pan from the heat. Cool
completely.

In a large bowl, combine the flour, sugar, and salt. Scatter the
butter over flour mixture. Toss well.

Cut the butter into the flour mixture using a pastry blender or 2
knives until the pieces become pea-sized.

Sprinkle the cheese over the mixture. Cut in briefly.

Sprinkle 3 tbsps. of the water over the mixture, toss well with a fork
to dampen. Add 3 tbsps. of the remaining water, 1 tbsp. at a time.
Using your fingers, continue to toss and mix by lifting the mixture up
from the bottom of the bowl on the upstroke and gently pressing down
on the downstroke.

Test the pastry by squeezing some of it between your fingertips. If it
seems a little dry and not quite packable, add more water, 1 tsp. at a
time, and work it in with your fingertips.

Form pastry into 2 balls, one should be slightly larger than the
other. Wrap in plastic wrap until ready to use. Chill for an hour if
pastry is too soft to work with.

Preheat oven to 375 degrees F.

Lightly butter a 9-inch pie plate.

Unwrap the larger pastry dough and place in between 2 large sheets of
parchment or wax paper. Tamp down the dough with the rolling pin and
gently begin to roll it out into a circular shape by rolling evenly in
one-eighth turns, until the dough is rolled out to an even thickness
of about 1/8-inch. Do the same with the other dough.

Remove the top sheet of paper from the larger dough. Place the pie
plate, upside-down, on top of the pastry. Turn the pie plate,
including the pastry, gently until they're rightside-up. Center and
fit the dough in the pie plate. Pierce the dough in several places
with the tines of a fork.

Fill with the apple mixture.

Dot the top with the remaining 3 tbsps. of butter.

Remove the top sheet of paper from the smaller dough. Place the dough
upside-down on top of the mixture, centering it on the pie plate.
Remove the other sheet.

Using your hands, crimp the edges of the 2 doughs together to seal.

With a sharp knife, make several cross slits on the top crust. Brush
with the egg wash and bake for 35 to 40 minutes.

Remove from the oven and cool for at least 20 minutes.