Preheat oven to 425 degrees.
Place peas and carrots, green beans, and celery in a pot, cover with water, and bring to a boil. Simmer for about 8 minutes till tender. Drain and set aside.
Sauté the butter and onions in the same pot until the onion is translucent, about 5 minutes. Stir in the flour, salt, pepper, garlic powder, and Italian seasoning. Slowly whisk in the chicken broth and milk. Bring it to a simmer and keep whisking until it thickens. Remove from heat.
Stir the cooked vegetables and cubed chicken into the gravy until well combined.
Place two pie crusts in the bottom of two 9 inch pie pans. Spoon the filling into the crusts filling them to the top. (I usually have leftover filling which is super yummy to eat on its own!) Top each pie with a crust and cut slits into them to allow the steam to escape while baking. Crimp the edges.
Brush the beaten egg on top of each crust with a pastry brush.
Bake at 425 degrees for 15 minutes and then at 350 degrees for 30 minutes.