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. Serve warm.