Step 1Put celery root, parsley root and potatoes in 3-quart saucepan; cover with water and add salt. Bring to boil. Reduce heat, cover and simmer until very tender (test parsley root, as it takes the longest to soften), about 25 minutes. Drain in colander. Return to pot over medium heat to dry out mixture, shaking pot often, about 5 minutes.
Step 2Mash vegetables with masher or ricer. Add milk or broth and butter. Season with peper to taste. Beat with whisk until fluffy. Serve hot, garnished with minced parsley (if using).