Preheat the oven to 350 degrees Fahrenheit. Cut the cornbread into 1-inch cubes. Spread onto a baking sheet and bake for 8 minutes to get toasted.
In a large bowl, whisk the broth and eggs together. Set aside.
Heat butter in a large skillet over medium-high heat. Add the onion, celery, thyme, sage, parsley, salt, and pepper. Cook for 4 minutes until vegetables are soft. Cook the sausage and cook until cooked through.
Pour the sausage mixture into the broth + egg, including any liquid from the skillet. Add the toasted cornbread cubes. Gently fold together.
If used to stuff a turkey, allow it to cool completely before stuffing. If baking separately, spoon stuffing into a greased baking pan. Bake for 30 minutes or until lightly browned and crisp on top.