To make the sauce: In a saucepan, combine the potato, carrot, garlic, and cashews with enough water to cover. Place the pan over high heat and bring to a boil. Cook until the vegetables are tender, about 10 minutes. Reserve 2 cups (480 mof the cooking water. Drain and transfer the cooked vegetables and cashews to a high-speed blender, along with the reserved cooking water.
Add the nutritional yeast, olive oil, paprika, miso, and lemon juice and season with salt and pepper. Blend until smooth. Taste and adjust the seasoning, as needed. Set aside.
To make the pasta: Bring a large pot of salted water to a boil over high heat. Add the pasta and cook according to the package directions until al dente. About 5 minutes before the pasta is done, add the broccoli to the pot. Drain the pasta and broccoli and return them to the pot.
Place the pot over low heat and add the scallions, spinach, and cherry tomatoes and toss to combine.
Pour the sauce over the pasta and vegetables and toss to combine and heat through. Transfer to a large serving dish and serve hot, garnished with sunflower seeds and basil leaves, if using.