Place cauliflower, potatoes and a big pinch of kosher salt in a large pot and add enough water to come just below the top of the vegetables.
Bring to a boil over high heat and then lower to a simmer. Cook until tender, about 15 minutes.
Drain cauliflower and potatoes and transfer to the bowl of a food processor fitted with the metal blade. Add butter and salt and process until smooth. Taste for seasoning and serve immediately.