Heat 2 Tablespoons canola oil over medium heat in a large skillet or saute pan. Add 1 cup yellow onion, 1 cup peeled, diced carrots, 1/2 cup diced celery, and 1/2 teaspoon kosher salt. Cover and cook for about 5 minutes. Remove the lid, stir, and continue to cook until the vegetables are beginning to soften, about 3-5 more minutes.
Stir in 2 teaspoons Better than Bouillon Roasted Chicken Base, 2 cloves garlic, 1/2 teaspoon freshly ground black pepper, and 1/2 teaspoon dried thyme and cook until fragrant, about one minute. Sprinkle 2 Tablespoons all-purpose flour over the vegetables and stir until the flour is evenly coating all of the vegetables. Cook for 2 more minutes.
Very slowly (starting with about 2 Tablespoons at a time) add 1 cup water, scraping up any browned flour from the pan and making sure to stir in all of the liquid after each addition. Initially, the mixture will be very pasty and hard to stir, but keep adding small amounts of liquid and stirring, and it will start to loosen up and resemble gravy. Stir in the 12 ounce can evaporated milk and bring to a simmer.
Stir in 1 pound leftover cooked chicken and cook until heated through, about 2-3 minutes. Remove the skillet from heat and stir in 1 cup frozen peas.
Move oven rack to middle position and heat oven to 425°F.
Roll out one of the pie crusts and lay it in a 9" pie plate. Trim off any excess if needed. Spread the chicken mixture into the crust in the pie plate. Roll out the second pie crust and place it on top of the filling. Crimp the edges of the two crusts together (I find the easiest way is to gently press the edges with the tines of a fork all the way around the crust).
Whisk together the egg with 1 Tablespoon of milk. Brush a little of this mixture all over the top and edges of the crust (make sure not to use so much that it forms pools). Save the rest of the egg for baking or making scrambled eggs, if desired. Cut a few slits in the top crust to make steam vents.
Place a pie shield over the edges of the crust (if you don't have one, you can use aluminum foil - see notes). Place the pie plate on a baking sheet and bake for 30-35 minutes, until the crust is golden brown and the filling measures 165°F. Keep an eye on the pie while it cooks. If you find that the top of the crust is browning too quickly, cover the whole pie with a sheet of foil. Note that if your pie plate is glass, you might have to add 5-10 minutes on to the cooking time.
Remove the pie from the oven and let cool for at least 10 minutes before cutting.
Notes
To make a foil pie shield: cut a round piece of foil slightly larger than the top of the pie. Cut an X in the center of the circle, and place the foil on top of the pie. Gently roll the points of the X outwards so that the middle of the pie is exposed, and only the edges of the pie are covered with the foil. Alternatively, cut 2-3 strips of foil, and lay them over the edges of the crust, gently folding the edges of the foil over the rim of the pan to secure.Make Ahead Instructions:To prep your chicken pot pie ahead of time, prepare the filling to the end of step 4. Transfer the filling to the fridge and keep it there for up to two days in an airtight container.When you're ready to bake, resume the recipe at step 5 and complete it. The pie will need to cook for an extra 5-10 minutes because the filling will be cold when you start baking.You could also prepare two pies at once, and freeze one for later. Don't thaw the pie before cooking, but cook it at a lower temperature for longer to ensure that the filling heats without the crust burning. Cook at 375° for 60 minutes. Check the temperature with an instant-read thermometer. The middle of the filling should read 165°F.