Crust: See note 1.In a large bowl, stir together the flour and salt. Using a pastry cutter (or 2 table knives), cut the butter into the dry ingredients until the mixture resembles coarse bread crumbs. In a separate bowl, whisk together the egg yolks and water (start with less water and add more as needed) until smooth. Pour into the center of the dry ingredients and stir with a wooden spoon until combined as much as possible. Gently knead with your hands to form a dough (add an extra tablespoon or 2 of water if needed). Handle the mixture as little as possible, and once it’s formed into a dough, gently flatten it into a disc. Cut the disc exactly in half and form each half into a smaller disc. Wrap each disc tightly in plastic wrap. Refrigerate for at least 30 minutes to allow the gluten to relax before rolling. You can make the crust ahead of time and refrigerate for 1–5 days.
Preheat oven to 400°F. Add the diced potatoes to a pot (you can peel if desired), cover with water and bring to a boil. Cook until tender, about 10–15 minutes. Remove from heat, drain and set aside.
Meanwhile, heat the butter in a large skillet or pot over medium-high heat. Once butter is melted, add the onions, cook for 2–3 minutes, and add garlic. Stir in the carrots and celery and cook until tender, stirring occasionally, about 6–8 minutes. Don’t rush this or you’ll have hard pieces of carrot/celery in the pot pie; they don’t get much more tender throughout the rest of the process.
Whisk in the flour and cook for about 1 minute to cook off the raw flavor. Gradually add the chicken stock and heavy cream, whisking constantly until the sauce is smooth. Next, stir in the salt, pepper, thyme, parsley, celery seed, and chicken bouillon powder. Simmer sauce over medium-low heat for 6–8 minutes or until sauce has thickened.
Gently add in diced chicken, peas, corn, and drained cooked potato. Remove from heat and set aside while you roll out the pie dough.
Roll out the pie crust on a lightly floured surface. Turn the dough about a quarter turn after every few rolls until you have a 12-inch circle of dough. Use the rolling pin to lift up the dough and gently place into a 9-inch pie pan (preferably glass or ceramic; avoid metal). Pour the pot pie filling into the crust. Add top crust. Gently tuck it in with your fingers, making sure it is smooth and the crust is fully sealed; then crimp the edges of the crust.
With a sharp knife, make a few small slits (to let steam escape) in the center of the top crust. Using a pastry brush, brush the crust and edges with beaten egg white. Bake for 45 minutes, or until the crust is golden brown. (Use a pie shield to protect the edges from browning too much if needed). Cool for 10–15 minutes; cut into slices and serve.
