Preheat the oven to 375°F (190°C). Line a sheet pan with parchment paper.
Spread the broccoli out on the prepared pan, and season with 1⁄4 teaspoon salt and 1⁄8 teaspoon pepper. Bake at 375°F for 15 to 20 minutes or until tender and beginning to brown on top but still firm.
Meanwhile, add the potatoes, 3 cups (720g) water, onion, and 1⁄2 teaspoon salt to a pot over medium heat. Bring to a simmer, and cook until the potatoes are tender, about 10 minutes.
Meanwhile, add the cashews, tomato sauce, yogurt, vinegar, paprika, remaining 1 teaspoon salt, remaining 1⁄4 teaspoon pepper, and, if desired, cayenne and nutritional yeast to a high-powered blender or food processor (see Note), and blend until completely smooth. Scrape the sides as needed. Set aside.
Once the cooked potatoes are tender, immediately remove the pan from the heat. Add the potato mixture, including the water, to the blender. Blend until completely smooth. Be careful not to overblend or the starch in the potatoes will release too much and make the texture too glue-like. You only need to blend until just combined. Taste and add more salt or spices, if desired.
Pour in bowls and top with the roasted broccoli. Garnish with cubed bread and fresh green onions, if desired.
Notes
If you do not have a high-powered blender like a Vitamix, you’ll need to soak your cashews for 8 hours or preferably overnight in a bowl of warm water to soften, and then drain, rinse, and proceed with the recipe. Otherwise, the soup will be gritty. If using soaked cashews, a food processor works better than a regular, non-high-powered blender. Alternatively, you can sub with raw cashew butter for the same amount, 114g, which is about 7 tablespoons. If using store-bought, make sure to use a raw cashew butter with no added oil.