Peel celery roots and cut into 1-in. pieces. Put in a large pot. Scrub potatoes and cut into 2-in. pieces; add them to pot with celery roots. Cover vegetables with cold water and bring to a boil.
Add 1 tbsp. salt and cook until vegetables are tender when pierced with a fork, about 10 minutes.
Drain well.
Transfer hot vegetables to a large bowl and mash with a potato masher or a large fork.
Add butter and cream and stir to combine well. Season with salt and pepper to taste.