In a large saucepan, combine chicken, carrots, and celery. Add water to cover and boil for 12 minutes. Remove from heat, drain, and set aside.
In a large skillet, melt the butter over medium heat. Add in the onions and sauté until translucent, about 5-7 minutes. Add in the garlic and cook for another 30 seconds.
Whisk in the flour. Then stir in the chicken broth, bouillon cubes, half and half, and fresh thyme. Bring to a simmer, and cook until thickened and the bouillon cubes are dissolved, about 5 minutes.
Stir in the cooked chicken and vegetables, frozen peas, parsley, and pepper. Remove from the heat.
Carefully place the first pie crust in the bottom of a 9-inch pie plate. With one hand, gently lift the corners of the crust and use your other hand to nestle the crust into the corners of the pie plate.
Pour the pot pie mixture into the crust.
Cover with the second pie crust, trimming off any overhang. Fold the edges of the crust under and crimp between two fingers. Brush the crust with the beaten egg. Cut a few slits into the top crust. Bake for 35-40 minutes or until the top crust is golden. If the edges begin to get too brown, cover them with a pie crust shield or aluminum foil.
Feel free to use store bought pie crust. Double check that the package contains two crusts – you’ll need them both. The night before, transfer the crust to the fridge to thaw overnight.
Make ahead: Cook the filling and let cool completely to room temperature. Fit the bottom crust into the pie plate and spoon in the filling. Top with the second crust, and crimp the edges. Wrap securely in plastic wrap and then aluminum foil. Freeze for up to 3 months. The night before cooking, transfer the pot pie to the fridge to thaw. Proceed with baking instructions the next evening.
Leftovers will keep well in the fridge for 3 to 4 days and can be reheated in the oven, covered with foil at 350F til heated through.