Place the celery root in a large pot and cover it with the milk by a few inches. (You may not need to use all the milk.) Add a few pinches of salt along with some freshly grated nutmeg. Bring to a gentle boil and simmer until the celery root is fork tender, 20 to 30 minutes. Drain, reserving about 1/4 cup milk, then return the celery root to the pot.
Place the pot over medium heat and let the celery root dry out for a minute or 2. Add the reserved milk and mash or puree using a potato masher or blender until very smooth. Check for seasoning, adding more salt if necessary.