Skillet Chicken Pot Pie with Puff Pastry Crust

Name: Skillet Chicken Pot Pie with Puff Pastry Crust
Ingredients: 4 tablespoons unsalted butter; 4 carrots , peeled and sliced ¼ inch thick; 2 celery ribs , cut into ¼-inch pieces; 1 onion , chopped fine; Salt and pepper; 1 teaspoon minced fresh thyme or ¼ teaspoon dried; 6 tablespoons all-purpose flour; 2 cups chicken broth; 1½ pounds boneless, skinless chicken breasts , trimmed; ½ cup frozen peas; ¼ cup heavy cream; 3 tablespoons minced fresh parsley; 1 tablespoon dry sherry; 1 (9 ½ by 9-inch) sheet puff pastry , thawed; 1 large egg , lightly beaten with 2 tablespoons water