Preheat the oven to 350℉ and grease a standard 9"x13" casserole pan.
Use your hands to break the cornbread into chunks and crumbles, and place in a large mixing bowl. (PRO TIP: The cornbread will break apart a little more when mixed with the other ingredients, so don't make the crumbles too small.)
Heat the olive oil in a large skillet over medium heat. Add the Italian sausage, breaking the sausage into pieces with your spoon or spatula. Cook, stirring frequently, until browned and cooked through.
Drain the crumbled, cooked sausage on a paper towel-lined plate, and discard about half of the cooking grease.
Return the skillet to the stove. Cook the onion, apples, and celery over medium heat until the onions are translucent and the celery and apples are lightly softened.
Add the sausage, celery/apple/onion mixture, chicken broth, belted butter, herbs, salt, and pepper into the large mixing bowl with the crumbled cornbread. Mix just until fully combined. Taste for seasoning.
Pour the cornbread dressing mixture into the casserole pan and bake, uncovered, for around 45 minutes, or until golden brown. Serve warm.