Preheat oven to 400°F.
Heat butter or oil in a large pot over medium heat. Then add onions, celery, thyme, garlic, and carrots. Cook and stir for about about 6-7 minutes until tender.
Stir in flour until it has been fully incorporated, stirring for about a minute. Gradually stir in half and half and broth.
Bring to a boil, stirring constantly. Cook and stir for about 2 minutes or until thickened and bubbles.
Gradually add in cooked chicken, peas, Creole seasoning, and parsley – remove from heat. Adjust salt, pepper, and seasonings to taste.
Unroll the pie crusts. Cover the bottom of the casserole and reserve the rest for the top.
Place the chicken mixture into a 2-quart casserole or desired baking dish. Cover with remaining pastry. Trim, seal, and flute edges. (You may freeze unbaked pies at this point or cut slits on the top for the steam to escape.)
Brush with egg wash mixture.
Bake in a preheated oven for 30-35 minutes or until pastry is golden brown and filling is bubbly and cooked through.