Place the potatoes in a pot large enough to also accommodate the carrots. Add enough water to cover the vegetables by 2 inches, sprinkle generously with salt, and bring to a boil. When the water has been boiling about 10 minutes, add the carrots and cook until both vegetables are "fork tender". Drain.
Bring the cream to a boil in a small saucepan. Meanwhile, pass the carrots and potatoes through a food mill into a large bowl. Add about one-quarter of the hot cream and 2 pats of the butter, stirring vigorously until thoroughly combined. Repeat this process until all of the remaining cream and butter have been incorporated. Taste for seasoning (you will probably have to add salt).
Serve immediately in a warm serving bowl or keep warm until ready to use.