Preheat your oven to 400°F (200°C). Let the pie crusts sit at room temperature for about 15 minutes before unrolling.
Carefully place one pie crust into a 9-inch pie dish. Press it gently into the bottom and up the sides. Trim any excess dough if needed, but leave about a 1/2-inch overhang.
Heat the olive oil or butter in a large skillet over medium heat. Add the chopped onion, carrots, and celery. Cook, stirring occasionally, until the vegetables begin to soften, about 5-7 minutes.
Stir in the salt, pepper, thyme, and garlic powder. Cook for another minute until fragrant.
Pour in the can of condensed cream of chicken soup and the milk (or broth). Stir well to combine and bring the mixture to a gentle simmer. Cook, stirring, for about 2-3 minutes until the sauce has thickened slightly.
Add the cooked chicken, frozen peas, and frozen corn to the skillet. Stir everything together until well combined and heated through.
Pour the chicken and vegetable mixture into the prepared pie crust in the dish. Spread it evenly.
Place the second pie crust over the filling. Trim the edges of the top crust to match the bottom crust's overhang. Crimp the edges together to seal the pie. Cut several slits in the top crust to allow steam to escape.
Brush the top crust evenly with the beaten egg wash. This will give your pot pie a beautiful golden sheen.
Bake in the preheated oven for 30-40 minutes, or until the crust is golden brown and the filling is bubbly. If the crust starts to brown too quickly, you can loosely tent the pie with aluminum foil.
Let the chicken pot pie rest for about 10-15 minutes before slicing and serving. This allows the filling to set properly.