Preheat your oven to 400°F (200°C).
Carefully unroll the pie crust and gently press it into a 9-inch pie dish. Crimp the edges if desired. If you're not using a bottom crust, you can skip this step and proceed directly to filling the dish.
In a large skillet or bowl, combine the cooked chicken, condensed cream of chicken soup, milk, thawed frozen vegetables, chopped onion (if using), salt, pepper, and thyme (if using). Stir everything together until well combined and the chicken and vegetables are evenly coated in the creamy sauce.
Pour the chicken mixture evenly into the prepared pie crust (or directly into the pie dish if not using a bottom crust).
If you are using a top crust, carefully unroll a second pie crust (or use the top half of your double-crust package) and place it over the filling. Crimp the edges to seal, and cut several slits in the top crust to allow steam to escape.
For a golden-brown finish, brush the top crust (or the edges if only using a bottom crust) with the beaten egg wash.
Bake 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 pot pie cool for about 10 minutes before slicing and serving. This allows the filling to set slightly.