Preheat oven to 350°F (175°C). Grease a 9×13-inch buttered baking dish and set aside. Chop or crumble day-old cornbread into a large bowl.

In a large skillet over medium heat, cook the sausage, breaking it up with a spoon, until browned and fully cooked through (about 6–8 minutes). Transfer to a large mixing bowl.

In the same skillet, add oil or butter if needed. Sauté the onion and celery for 6–8 minutes, until softened and translucent. Add garlic and cook for 30 seconds more. Transfer the vegetables to the bowl with the sausage.

Add the crumbled cornbread, rosemary, oregano, parsley, salt, and black pepper to the bowl with the sausage onion celery mixture and gently toss to combine.

In a separate bowl (or medium bowl), beat the egg then whisk together with the chicken broth. This is your egg mixture.

Transfer the cornbread mixture to the prepared baking dish and spread evenly without pressing down too firmly. Pour the egg and broth mixture over the cornbread mixture in the baking dish. Gently fold everything together until evenly moistened. Add additional broth as needed. The mixture should be moist but not soggy. (Yes, this can be mixed in a bowl then scooped into the casserole dish id you prefer.)

Cover loosely with aluminum foil. Bake dressing at 350°F for about 30 minutes covered. Cornbread stuffing should be baked covered for the first part to steam the interior. Then remove the foil during baking to achieve a crispy top, and bake another 15–20 minutes until the center is set, the edges are golden brown, and an instant-read thermometer reads 165°F.

A resting time of about 10 minutes after baking allows for easier serving. The dressing firms up as it cools slightly.