Line the inside of a 9-inch pie dish with one of the pie crusts, allowing it to hang over the sides.
In a large skillet, melt the butter over medium-heat. Cook the onion and celery in the melted butter for about 5 minutes, until softened.
Stir in the flour, and cook for an additional 5 minutes. Stir in the broth, milk and seasoning, stirring constantly. Continue to cook until the sauce has thickened. Taste, and add salt and pepper, to taste. Stir in the turkey and vegetables; turn off the heat.
Pour the pie filling into the prepared pie dish, spreading out evenly.
Brush the edges of the bottom pie crust with the beaten egg. Lay the 2nd pie crust over the top, and pinch the edges to seal. Brush the top lightly with the egg, then cut some slits into the top pie crust for the heat to escape while cooking.
Bake for 35 to 40 minutes. Keep an eye on it, and if it looks like the pie crust is getting too dark, line the edges with foil.