Place a large sauté pan over medium heat. Add the butter and pork sausage. Break the sausage into small pieces with a wooden spoon and cook for 3-5 minutes.
Add the onions and celery. Cook for a couple minutes, then stir in the mushrooms. Sauté until the sausage is cooked through and the mushrooms are soft, about 5 more minutes. Stir in the fresh chopped herbs, then turn off the heat.
Beat the eggs and chicken broth together and season with 1 1/2 teaspoons salt and 1/2 teaspoon ground black pepper. Stir the broth mixture into the sausage and mushroom mixture.
Fold the bread cubes into the sausage mixture, making sure the cubes are well coated in broth.
Spoon the stuffing into the prepared baking dish. Spread it out evenly, then sprinkle the top with Parmesan cheese. Bake for 45 minutes, or until puffed and golden in the center. Serve warm.
This recipe can be made up to 2 days ahead if needed, then reheat on Thanksgiving. However, I prefer to prep the ingredients ahead, leaving the broth and egg mixture separate from the rest. Then combine all ingredients and bake right before serving.