Preheat the oven to 350 degrees F. Butter a 15 by 10 by 2-inch glass baking dish.
Melt 2 tablespoons of butter in a large heavy 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 plate lined with a paper towel.
Melt the remaining butter in the same skillet over medium-high heat. Add the onions, carrots, celery, garlic, rosemary, and mushrooms. Season with salt and pepper, to taste. Saute until the onions are very tender, about 12 minutes.
In a large bowl, add the sauteed vegetables, the chestnuts, Parmesan and bread. Add enough broth to the stuffing mixture to moisten. Add the cooked pancetta and eggs. Season the stuffing, to taste, with salt and pepper and add the parsley. Stir to completely combine all the ingredients.
Transfer the stuffing to the prepared dish. Bake until the stuffing is heated through and the top is golden brown, 30 to 45 minutes. Remove from the oven and serve.