1. Put the pearl onions in a large bowl. Add the carrots and potatoes to a medium pan of boiling water and simmer for about 10 minutes, or until tender. Drain and add to the onions.

2. In a medium skillet, melt 2 tablespoons of the butter over medium heat. Add the leeks and sauté for about 3 minutes, or until softened. Add the mushrooms and sauté for 3 minutes, or until softened. Add the leeks and mushrooms, along with the cooking juices, to the vegetables in the bowl. Add the peas, corn, and turkey, mix well, and set aside.

3. Preheat the oven to 400°F. In a large saucepan, melt the remaining 6 tablespoons butter over medium heat. Sprinkle in the flour and cook, whisking constantly, for 3 minutes or until the roux is blond colored. Slowly add the broth and half-and-half, whisking constantly, and whisk for about 3 more minutes, until the sauce is thickened and smooth. Season with salt and pepper. Pour the sauce over the turkey mixture, add the herbs, and mix well. Taste for seasoning.

4. Butter a large 2-inch-deep casserole dish (about 9 by 13 inches). Pour the turkey mixture into the casserole.

5. If necessary, rollout the pastry on a lightly floured surface to a 14-by-10-inch rectangle. Brush the rim of the casserole dish with water. Cover the filling with the pastry, pressing it against the rim of the dish. Make 3 slashes in the pastry. Brush the crust with the beaten egg.

6. Place the dish on a baking sheet and bake for 40 to 45 minutes, or until the filling is bubbling. Sprinkle with the Parmesan cheese during the last 15 minutes of baking to brown the crust. Let the potpie sit for 10 minutes before serving.