Chicken Pot Pie with Cheesy Crust

This is a real comfort food dish, but really no weeknight affair. This takes some time - great for a weekend, and is worth every minute of toil - a real act of love. Our daughter insisted we put a crust on the bottom of the pie, and I couldn't agree more. Baking at relatively high temperature for a short time at first seems to brown the outside of the bottom crust. Very yummy.
1 whole chicken, cut up
3 carrots, sliced
3 stalks celery, diced
1 onion, diced
2 cloves garlic, minced
2 tsp hebes de Provence
1/2 cup peas
3 Tbsp corn starch

Cheesy crust:
3 cups flour
2 tsp salt
1/2 tsp dried dill
1 1/2 sticks butter, sliced and chilled in freezer for a few minutes
4 oz. herbed feta cheese, crumbled
4 oz. grated cheddar cheese
6-8 Tbsp ice-cold water

Egg wash:
1 egg whisked together with 1 Tbsp water

Prepare the chicken by browning in a large pot in a bit of olive oil, about 5 minutes, until all pieces begin to brown. Add carrot, celery, onion and garlic and cook another 10 minutes, until the veggies begin to soften and become very fragrant. Salt an pepper to taste while you sauté the veggies. Add about 6 cups of water - just enough to barely cover the chicken. Bring to a boil, then reduce to a simmer. cover and cook for about 30-45 minutes, until the chicken just begins to fall off the bone. Stir to redistribute the chicken from time to time.

Meanwhile prepare the crust by mixing the flour with the salt and dill in a food processor fitted with a steel blade. Add the chilled butter slices to the flour, pulsing just until the butter is incorporated coarsely into flour. Add the cheeses and pulse a few more times just to incorporate. With the processor running, add enough of the water to make the dough just about to form a rough ball. Stop processing immediately - do not over mix the dough. Carefully transfer the dough onto a counter, divide and press together to form two balls of dough. Wrap each in plastic and refrigerate for half an hour.
Preheat the oven to 400F. Let the chicken broth mixture cool a bit and then strain the chicken into a colander seated in a large enough bowl to hold it. Remove the colander and let the meat cool enough to shred the meat from the bones. Separate out as many of the veggies as you can, and set aside. You should have about 4-5 cups of stock; if not, bring up to 4 cups with water. Dissolve the corn starch in 3 tablespoons of cold water in a small bowl. Bring the stock to a boil and whisk in the cornstarch. Allow stock to thicken - adjust with a bit more cornstarch dissolved in water to thicken further if necessary - depending on how much stock you have. Tip in the peas to heat through, then fold in the veggies and the chicken. Set gravy aside.

Grease a 2-quart oven-going casserole. Roll out the balls of dough to circles big enough to fit the casserole. Line the bottom of the casserole with one dough sheet. Pour in the chicken filling. Cover the filling with the second sheet of dough. Lightly brush the crust with egg wash. Pierce several tiny holes into the crust for venting. Bake for 20 minutes. Reduce heat to 350F and bake for another 20 minutes, until crust is nicely browned and gravy begins to bubble through holes.