Preheat the oven to 275 degrees F. Distribute the diced cornbread evenly on a baking sheet and dry out in the oven for 45-50 minutes. Place in a large bowl and set aside.
In a large skillet, heat the olive oil over medium heat and add the sausage. Cook for several minutes, allowing the pieces to caramelize. Once they are nicely browned, move them to a paper towel-lined plate and set aside. Drain some but not all of the fat from the pan and then add the diced onion and celery with a pinch of salt. The liquid from the vegetables should help loosen up any brown bits on the bottom of the pan; stir those in with the vegetables. Cook for 3-5 minutes until the onions are slightly caramelized. Add the garlic, thyme and sage and cook for another minute before removing from the heat. Stir in the salt and pepper.
Whisk together the chicken stock, half and half and egg. Pour the mixture over the cornbread. Add the sausage as well as the vegetable mixture and fold the ingredients together. Cover with plastic wrap and allow the ingredients to chill in the refrigerator for one hour.
Preheat the oven to 400 degrees F. Grease a 9x9 inch baking dish and distribute the stuffing ingredients evenly. Bake for 45-50 minutes, until the top is golden brown.