Preheat oven to 375.
In a large skillet melt butter over medium/high heat. Add onion, carrots and celery and cook 3-4 minutes, just until onions begin to soften.
Sprinkle flour over vegetables and stir, let cook just 1 minute (to cook out the flour flavor). Add broth and stir well to dissolve the flour.
Once broth starts to thicken, add chicken and seasonings then stir and add milk. Cook another 3-4 minutes. If gravy seems too thick, add a little more broth. Taste for seasoning and add if necessary.
Press 1 defrosted pie crust into the bottom of a 9 inch pie dish, letting the extra crust hang over the edge.
Pour filling into crust and top with remaining crust. Make sure to press the edges together well to seal everything in.
In a small bowl, beat egg and water together. Brush mixture over top of pie crust. Cut 2-3 tiny slits in top of crust to vent.
Place pie on a rimmed baking sheet and bake 25-30 minutes.
Serve over mashed potatoes.