Heat oven to 425°F; fit one crust into a 9-inch pie dish.
Melt butter in a large skillet over medium heat; sauté onion and celery until softened, about 5 minutes.
Stir in flour; cook 1-2 minutes. Gradually whisk in broth and cream, stirring constantly until thickened.
Stir in chicken, peas and carrots, poultry seasoning, salt, and pepper until combined and heated through.
Pour into crust; cover with second crust and seal and crimp edges.
Cut 4-5 slits in top; brush with egg and bake 30-35 minutes until golden brown.
Cool 10 minutes before serving.