Heat the oven to 275°F and arrange a rack in the middle.
Using your hands, crumble the premade cornbread into pieces no larger than 3/4 inch onto a rimmed baking sheet. Spread into an even layer and bake for 15 minutes. Turn off the oven and let the cornbread dry out inside the oven overnight.
The next day, transfer the cornbread to a large bowl and set it aside.

Heat the oven to 350°F with the rack in the middle. Coat a 13 x 9-inch baking dish with butter; set aside.

Melt 1 1/2 sticks of the measured butter in a large frying pan over medium-high heat. Add the celery, celery root, and onion, season with salt, and cook, stirring occasionally, until softened, about 10 minutes.
Add the thyme and celery seeds and cook, stirring occasionally, until fragrant, about 1 minute. Season with salt and pepper and transfer to the bowl with the cornbread.
Drizzle the stock or broth and the oyster liquid into the bowl and stir until completely incorporated. Fold in the oysters, eggs, and parsley.
Transfer the stuffing to the prepared baking dish. Cut the remaining 1/2 stick of butter into small pieces and scatter them over the top of the stuffing. Bake until golden brown on top, about 40 minutes.