Toss the rutabagas into a large pot and cover generously with water. Season the water generously with salt.
Bring the water to a boil, reduce to a simmer and simmer for 45 minutes. Toss in the potatoes and simmer until the potatoes are fork tender, another 20 minutes.
Strain the rutabagas and potatoes from the water and pass through a food mill into a large bowl.
In a small saucepot, bring the cream to a boil and turn off.
Take 1 to 2 pats of butter and a splash of hot cream and whip them into the potato mixture. Continue this until all the butter and cream are incorporated. Taste and re-season with salt if needed. Serve immediately or keep warm in a low oven.