Put the celery root and potatoes in a large saucepan and cover with salted water. Bring to a boil, then reduce heat to medium and cook until tender, about 15 to 20 minutes. Drain, press through a food mill or ricer, then return the potatoes to the pot. Add the butter and stir and mash until it melts completely. Add the half and half and stir to mix. Season with salt and pepper to taste and serve hot.