Simmer chicken in water with salt for 1 hour. Cool and pick meat from bones. Set aside. Skim fat from broth and reserve 2 cups broth. Sauté onion, carrots, celery, and potato in butter until tender.
Add flour, stir until smooth. Gradually add reserved broth and half-and-half. Cook over medium heat, stirring constantly until thickened and bubbly. Stir in chicken, salt and pepper to taste.
Preheat oven to 400° F. Pour mixture into 11x7x2-inch baking dish. Shape pastry to fit. Top with pastry and crimp edges. Cut small slits in top. Bake for 30 minutes until golden brown.Servings: 8