Place the potatoes in a pot large enough to accommodate the celery root and the potatoes. Add enough water to cover the vegetables by 2 inches and season generously with salt. Bring to a boil and cook for about 10 minutes. Add the celery root and cook until both vegetables are fork tender. Strain the celery root and potatoes.
Pour the cream in a small saucepan and bring to a boil. Meanwhile, pass the celery root and potatoes through a food mill into a large bowl. Add one-quarter of the hot cream and 2 pats of the butter. Stir vigorously until the cream and butter are thoroughly combined. Repeat for the remaining cream and butter. Taste for seasoning, you will probably have to add salt. Serve in a warm serving bowl immediately or keep warm until ready to use.