Preheat the oven to 400°F. Peel or scrub the sunchokes. Cut the sunchokes into half-inch cubes. Cut the cauliflower into florets. Place the vegetables on a rimmed baking sheet. Drizzle over the olive oil, sprinkle on the salt and toss to coat. Roast for about 50 minutes until they are golden brown and very tender.
Transfer the vegetables to a food processor, add 2 cups of the broth, and puree until fairly smooth. Return the puree to the pot over medium heat, add 2 cups of additional broth, or more depending on the desired consistency. Bring to a simmer over medium-high heat. Stir in the 1/4 cup Parmesan and the cream and serve the soup hot in mugs or bowls. with the scallions sprinkled over and additional Parmesan passed on the side.
Notes
The first time I made this soup it was without the few glugs of cream stirred in at the end. I thought it was good, but with the cream I think it’s much better. The amount of broth is really dependent on how thin or thickly porridge-like you want your soup to be. Make sure to use vegetable broth (store-bought or homemade) if there are vegetarians in your family or at your table.