Sauté onion, celery, carrots, and potatoes in butter for 10 minutes. Add flour to sautéed mixture, stirring well. Cook 1 minute, stirring constantly. Combine broth and 1/2 cup of half-and-half. Gradually stir into vegetable mixture. Cook over medium heat, stirring constantly until thickened and bubbly. Stir in salt and pepper, then add chicken. Stir well. Pour into a shallow casserole dish.
Roll the pastry sheets to 1/8'' thickness. Cut pastry 1/2'' larger than the pan. Combine the egg yolk and 1 Tbsp half & half. Brush one side of the pastry. Place brushed-side-down over top of chicken mixture, folding edges under and pressing firmly to the sides of the casserole dish. Brush the top with the remaining egg mixture. Bake for 15-20 minutes until top is puffed and browned.
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