Preheat the oven to 350˚F (180˚C) if making dressing.
Preheat the oven to 325˚F (160˚C) if making stuffing.
Crumble the cornbread and biscuits into a large bowl. Set aside.
Thinly slice the sage and set aside.
Heat the olive oil in a large pan over medium-high heat. Add the sausage and cook until browned, 3-5 minutes.
Add the onion and celery, and cook until softened, 5-7 minutes.
Add the sage, rosemary, and thyme, and cook until fragrant, 3-4 minutes. Season with salt and pepper. Remove the pan from the heat and set aside.
In a medium saucepan over medium-high heat, combine the butter and chicken stock. Melt the butter completely and bring to a boil. Add the heavy cream and stir to combine.
Add the sausage mixture to the crumbled cornbread and biscuits, and mix to combine. Pour the chicken stock mixture, a bit at a time, over the bread mixture. Mix well.
If you are making dressing, transfer the mixture to a buttered 9x13-inch (23x33 cm) baking dish and cover with foil. Bake for 40 minutes, then remove the foil and bake for 10-15 minutes more, or until the top is lightly browned. Do not overbake.
If you are making stuffing, stuff the mixture into the cavity of a small turkey [12-14 pounds (5.5-.6.5 kilograms)]. Bake for 4-5 hours, or until the temperature of the stuffing reaches 165˚F (75˚C).
Serve warm with your favorite Thanksgiving dishes.