Cut cornbread into 1-inch cubes and place in large mixing bowl with 2 tablespoons of olive oil. Add 2 tablespoons of fresh thyme (1/2 tablespoon dried) and toss cornbread to coat.
Spread the cornbread out on baking sheets and bake until slightly toasted (about 15 minutes). Allow toasted cornbread to cool at room temperature for about 30 minutes, then return to bowl.
Meanwhile, in a large skillet, brown sausage over medium heat until cooked through. Use a slotted spoon to remove sausage from the skillet (or drain grease) and add sausage to mixing bowl.
Heat remaining 2 tablespoons of olive oil and butter over medium heat and add onion and celery. Sauté onions and celery for about 10 minutes. Add dried cranberries or cherries to the onion and celery, and sauté for about 5 minutes. Fold the mixture into the bowl with cornbread and sausage.
Add the remaining thyme, sage, parsley to the mixing bowl and toss well with spatula.
Drizzle the mixture with chicken broth to moisten and add salt and pepper to taste.
Place into a baking pan, cover with foil and cook for 25-30 minutes.
Cook's Note: I prepare 3 packages of cornbread mix, bake according to directions, and allow to cool overnight.