Peel vegetables, rinse, and cut into 2-in. chunks. Put in a large saucepan with 1 tsp. salt and water to cover. Bring to a boil over high heat, then reduce heat and simmer until tender, 15 to 25 minutes. Drain.
Return vegetables to pot with remaining 1/2 tsp. salt, the butter, and cream. Mash (some lumps are okay). Season with salt to taste.