Preheat the oven to 350°F. Generously butter a 13- x 9-inch baking dish and set aside.
In a large skillet, cook the sausage until brown and the fat is rendered, about 5 minutes. Add the onions, celery, bell peppers, and garlic, and cook for 2 minutes. Remove from the heat and transfer to a large bowl to cool.
Crumble the cornbread into a mixing bowl. Add the torn bread, green onions, parsley, and thyme, and mix well with your hands. Add the salt, pepper, cayenne, and eggs, and mix well with your hands or a large wooden spoon. Add enough broth, 1/2 cup at a time, to moisten the dressing, being careful not to make it mushy.
Transfer the mixture to the prepared dish and cover with aluminum foil. Bake until heated through, about 25 minutes. Uncover and bake until golden brown, about 15 minutes.
Makes 8 servings
Preheat the oven to 400ºF.
Pour 1 tablespoon of vegetable oil into a 9-inch baking pan or heavy cast-iron skillet. Place the pan into the oven as it preheats, allowing it to heat for at least 10 minutes.
Combine the cornmeal, flour, baking powder, salt, and cayenne in a large mixing bowl and stir with a wooden spoon. Add the remaining 1/4 cup oil, the buttermilk and the egg to the mixture and stir well to blend.
Pour the cornmeal batter into the preheated pan and bake in the oven for 25 minutes or until lightly golden brown. Remove from the oven and let cool before serving or using in the dressing.
(Note: When making the dressing, make cornbread the day before.)
Makes one 9-inch round