Hearty Chicken Pot Pie

Name: Hearty Chicken Pot Pie
Prep time: 20 min
Cook time: 1 h
Total time: 1 h 20 min
Cuisine: American
Ingredients: 1.5 pounds skinless, boneless chicken breast meat; 1 cup chicken broth; 0.5 teaspoon salt; 0.25 teaspoon ground black pepper; 1.5 cups milk; 3 tablespoons butter; 1 onion, chopped; 1 cup chopped celery; 0.33333334326744 cup all-purpose flour; 2 cups frozen mixed vegetables, thawed; 1 tablespoon chopped fresh parsley; 0.5 teaspoon dried thyme; 1 (9 inch) pastry for a 9 inch single crust pie; 1 egg, lightly beaten