Preheat oven to 425°F and place one pie crust in a 9-inch pie dish.
In a large skillet over medium heat, melt butter and sauté onion and celery until softened, about 5 minutes.
Stir in flour and cook for 1-2 minutes, then gradually whisk in chicken broth and heavy cream, stirring constantly until thickened.
Add chicken, frozen peas and carrots, poultry seasoning, salt, and pepper, stirring until well combined and heated through.
Pour the filling into the prepared pie crust and top with the second crust, sealing and crimping the edges.
Cut 4-5 slits in the top crust, brush with beaten egg, and bake for 30-35 minutes until golden brown.
Let cool for 10 minutes before serving.