Place the celery root in a 2-quart saucepan. Cover the half-and-half, and add the butter and thyme. Bring to a boil over medium-high heat. Lower to medium-low and simmer, partially covered, until celery root is tender, about 25 minutes. Discard thyme. Transfer the celery root mixture to the bowl of a food processor and purée. Place a sieve over a clean saucepan, and scrape the purée through the sieve. Keep warm over very low heat.

Place potatoes and salt in a large pot and cover with water. Bring to a boil over high heat, lower to medium-low, and simmer 10-15 minutes, until potatoes are tender. Drain potatoes and use either a potato masher or a ricer to mash them. Transfer to the saucpan of celery root, and whisk in the cheese. Whisk until cheese is melted and the potatoes are smooth. Season to taste with salt and pepper.