Cut off the roots of the celery root, then peel and wash it. Cut it into medium sized chunks (about 4 cm to a side). Peel the potatoes and cut in the same size of chunks. Place the cut vegetables in a big pot and cover with cold water. Add a 1/2 teaspoon of salt to the cooking water.
Bring the vegetables to a low boil on medium heat and cook until tender - about 25 minutes. Drain the vegetables and puree them using your favorite method (potato masher, food mill, or food processor). Return them to the pot.
Warm the milk in a small pan and blend in the butter, nutmeg and salt and pepper. Mix it into the puree and serve hot.
Makes 6 servings.