Preheat the oven to 425 degrees. Butter a 9-inch by 13-inch baking dish. Place the cornbread into a large bowl.
In a large skillet over medium heat, melt the butter and oil. Stir in sausage and cook until lightly browned, about 5 minutes. Add onion and cook until translucent, about 2 to 3 minutes.
To the cornbread, add celery and sausage mixture and toss to combine. Add eggs, dried thyme, 1/2 teaspoon salt, 1/2 teaspoon pepper, and parsley. Stir in turkey stock, a little at a time, until it forms a moist mixture.
Place mixture in prepared baking dish and cover with aluminum foil. Place in the oven and bake, covered, for 45 minutes. Remove foil and bake until crispy, about 20 additional minutes. Serve.