Butter a 15 by 10 by 2-inch glass baking dish. Melt 2 tablespoons of butter in a heavy large skillet over medium heat. Add the pancetta and saute until crisp and golden, about 10 minutes. Using a slotted spoon, transfer the pancetta to a large bowl. Melt the remaining butter in the same skillet over medium-high heat. Add the onions, carrots, celery, rosemary, and garlic. Saute until the onions are very tender, about 12 minutes. Gently stir in the chestnuts and parsley. Transfer the onion mixture to the large bowl with the pancetta. Add the bread and Parmesan and toss to coat. Add enough broth to the stuffing mixture to moisten. Season the stuffing, to taste, with salt and pepper. Mix in the eggs.
Transfer the stuffing to the prepared dish. Cover with buttered foil, buttered side down, and bake until the stuffing is heated through, about 30 minutes. Uncover and continue baking until the top is crisp and golden, about 15 minutes longer.