CRUST: (NOTE 1) In a large bowl, combine the flour and salt. Stir. Using a pastry cutter (or two 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 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 two of water if needed). Handle the mixture as little as possible and once it's formed into dough, gently flatten into a disc. Cut the disc exactly in half and form each half into a small 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.
POTATO: Preheat the oven to 400 degrees 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.
FILLING: Meanwhile, heat the butter in a large skillet or pot over medium-high heat. Once the butter is melted, add the onions, cook for 2-3 minutes and then add in the 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 then the heavy cream, whisking constantly until the sauce is smooth. Next, stir in the salt, black 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 the diced chicken, frozen peas, frozen corn, and the drained cooked potato. Remove from heat and set aside while you roll out the pie dough.
ASSEMBLY: 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 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 crust is fully sealed and then crimp the edges of the crust.
BAKE: With sharp knife, make a few small slits 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 crust is golden brown. (Use a pie shield to protect the edges from browning too much too soon if needed). Cool for 10-15 minutes, cut into slices and serve.