Preheat the oven to 400℉. Toss the broccoli with a little oil and some salt and pepper and spread evenly on a large baking sheet. Roast for 20 minutes.
While the broccoli roasts, heat 2 teaspoons of olive oil in a Dutch oven or large pot over medium heat. Add onion and carrots and cook for 6-8 minutes until the vegetables are soft. Add the garlic and cook another 30 seconds.
Add the potatoes, broth, cashews, nutritional yeast, paprika, salt, and pepper and bring to a boil. Then reduce the heat to low, cover the pot, and simmer for 20 minutes until the potatoes are soft.
Allow the soup to cool a bit then transfer to a blender to puree it, working in batches if necessary. After the soup is pureed, add the roasted broccoli and pulse a few times, just enough to incorporate the broccoli without pureeing it.