Pat pork dry and season with kosher salt and pepper. Heat half of the oil in a 5-quart heavy pot over medium-high heat until it shimmers. Brown pork on all sides, 6–7 minutes, then transfer to paper towels to drain. Add remaining oil to the pot. Cook the onion, garlic, celery root, mushrooms and thyme. Season with salt and pepper. Stir occasionally until softened, 4–5 minutes.

Return the pork to the pot with the stock, wine and honey and bring to a boil. Reduce the heat to low and simmer, covered, stirring occasionally, until meat is very tender, 3–3½ hours. Using a whisk, break up the meat in the pot. Simmer ragù, uncovered, stirring frequently, 15 minutes.