Bring a pot of water to a boil. Salt it, add the carrots and celery root or parsnips, and cook until tender, about 10 minutes. Drain then transfer to a food processor and purée.
Meanwhile, bring a second large pot of water to a boil. Salt it, add the pasta and cook 2 minutes shy of al dente. Drain and return to the pot.
While the pasta is working, in a large saucepan, melt butter over medium heat. Add the onion and garlic, and cook for a few minutes, then whisk in the flour. Whisk in the milk and simmer until thickened, about 3 minutes. Season with salt, pepper and Old Bay. Add in 2 cups cheddar and melt, stirring in a figure-eight motion with a wooden spoon.