Fill a large bowl with ice water and add lemon juice. With sharp knife, peel celery root; cut into 2-in chunks, dropping them into the water and lemon juice as you go. (This stops the celery root from discoloring.)
Cut potatoes into 2-in chunks. Drain celery root. In large saucepan, combine celery root, potatoes, garlic and enough water to cover them. Bring to boil. Reduce heat to medium-low; cook, covered, 20 minutes or until celery root and potatoes are very tender. Drain well; return vegetables to saucepan. Place over low heat to dry out slightly, shaking saucepan occasionally.
Heat butter and cream in small saucepan; transfer to large bowl. Add vegetables to cream mixture and cream until smooth and creamy. Season with salt and pepper to taste; stir in parsley.
Transfer to heated serving dish; serve immediately.