1. Preheat oven to 425 degree F. Lightly butter 4 (1-1/4-cup) ovenproof bowls.
2. Melt butter in a large skillet over moderately high heat. Add onion, celery, and thyme; cook, stirring, until vegetables are softened, about 4 minutes. Transfer to a large bowl. Stir in green bean casserole, turkey, gravy, and broth; season with salt and pepper.
3. Unfold 1 pastry sheet and roll out on a lightly floured surface with a floured rolling pin into a 12- by 11-inch rectangle. Cut out 2 (6-inch) rounds. Keep pastry rounds chilled while repeating with remaining pastry sheet. Brush rims of prepared bowls with egg and divide turkey mixture evenly between them. Top each with a pastry circle, pressing edges against outside rim of each bowl to seal. Brush tops with egg and place a parsley leaf in center of each pie, brushing with egg to adhere. Chill pies until dough is firm, about 15 minutes.
4. Bake pies on a baking sheet in middle of oven until tops are puffed and golden brown, 12 to 15 minutes. Serve pies hot with spoons. Makes 4 servings.