- Place 1⁄2 cup butter in a 9×13-inch baking pan. Heat in oven at 425 degrees for 4 minutes.
- Combine cornmeal, flour, baking powder, and salt in a large bowl.
- Whisk in eggs and buttermilk.
- Pour hot butter into batter, stirring until blended.
- Pour batter back into 9×13-inch pan. Bake at 425 degrees for 30 minutes or until golden brown. Transfer cornbread to a cooling rack and cool completely. Crumble cooled cornbread into a large bowl and set aside. Reduce oven to 350 degrees.
- Heat oil in a large skillet over medium heat. Add sausage and cook 8−10 minutes or until browned. Remove sausage with a slotted spoon and set aside.
- Add onion and celery to the skillet and sauté 2 minutes. Add garlic and thyme and continue cooking for 5 minutes or until vegetables are softened.
- Spoon onion mixture into bowl with cornbread crumbles. Stir in sage, salt, pepper, cayenne, and reserved sausage.
- Whisk together broth, butter, and eggs and pour over cornbread mixture along with oysters and toss until well moistened.
- Spoon dressing into a lightly greased 11×15-inch (about 5-quart) baking dish and bake covered at 350 degrees for 30−35 minutes.
- Uncover and cook and additional 10−15 minutes or until golden brown and cooked through. Serve hot.