Marinate pork in garlic, salt, pepper, bay leaves and thyme for 8 to 12 hours. When ready to cook, preheat oven to 300 degrees F. Heat oil and brown pork on high heat in a large pot or Dutch oven, working in batches if necessary to brown all pieces well on all sides. Reduce heat to medium; add celery root, carrots, onion and brown sugar, and sauté, letting vegetables and pork caramelize. Add red wine to pot and simmer until reduced by half. Add stock, and cover with foil.
Transfer to oven and roast about 2 hours, until sauce is thickened and pork is fully cooked and able to shred easily. Meanwhile, stir together sour cream cream and horseradish.
Strain liquid from pot into a saucepan. Add a touch of water to 1/3 cup cornstarch to make a slurry. Add half to slurry to liquid and bring to a boil, whisking. Add more slurry if necessary to thicken.
To serve, place some vegetables on each plate, and top with a piece of pork. Top and surround with sauce, and add a spoonful of horseradish cream. Garnish with thyme if desired.