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.