Place the potatoes in a pot large enough to accommodate the celery root and the potatoes. Make sure to add enough water to cover vegetables by 2 inches and season generously with salt. Bring the water to a boil. When the water has been boiling for about 10 minutes, add the celery root and cook until both vegetables are "fork tender". Strain the celery root and potatoes.

Put the cream in a small saucepan and bring it to a boil. Meanwhile, pass the celery root and potatoes through a food mill into a large bowl. Add about 1/4 of the hot cream and 2 pats of the butter. Stir vigorously until the cream and butter are thoroughly combined. Repeat this process until all of the cream and butter have been incorporated. Taste for seasoning, you will probably have to add salt. Serve in a warm serving bowl immediately or keep warm until ready to use.