Preheat oven to 350°F (175°C). Butter a 9x13 inch baking dish.
In a large skillet over medium heat, brown the sausage, breaking it into smaller pieces as it cooks, about 5-7 minutes.
Add the onion, celery, and bell pepper (if using) to the skillet with the sausage. Cook until the vegetables are softened, about 5 minutes.
Stir in the garlic, sage, thyme, rosemary, marjoram, and black pepper. Cook for another minute until fragrant.
Pour in 1/2 cup of the chicken broth, stirring to scrape up any browned bits from the bottom of the skillet. Remove from heat and let cool slightly.
In a very large bowl, combine the dried cornbread cubes and the sausage mixture. Toss gently to combine.
In a separate bowl, whisk together the remaining 2 cups of chicken broth and beaten eggs.
Pour the broth and egg mixture over the cornbread and sausage, along with the melted butter and fresh parsley. Fold everything together gently until well combined. The mixture should be moist but not soggy. If it seems too dry, add a bit more broth; if too wet, add more cornbread.
Transfer the mixture to the prepared baking dish, spreading it out evenly.
Cover with foil and bake for 30 minutes. Then, remove the foil and bake for an additional 15-20 minutes until the top is golden brown and crispy.
Let rest for 10 minutes before serving.