Add cashews to a bowl of hot tap water and soak 30 minutes - 1 hour. Fill two pots 3/4 way full of water and bring to a boil. One pot should be at least 4 quarts and the other should be at least 6 quarts. Add 1/4 teaspoon sea salt to each pot.
To the smaller pot, add diced sweet potato and carrots, then bring down to a simmer. To the other pot, add pasta. Cook pasta according to package directions, MINUS 1-2 minutes, so noodles are slightly al dente. When pasta is drained and rinsed, set aside. *Note: if using Banza shells, like I did, I boiled them for 8 minutes. Now check your sweet potatoes and carrots—they should be knife-tender. Drain and rinse. Set aside.
Refill your 6 quart pot 1/2 way and bring to a boil again. Add broccoli florets and allow to boil 1 minute, then drain and rinse with cold water. Set aside. To a high powered blender, add cashews, sweet potatoes, carrots, onion, garlic, mustard, nutritional yeast, nut milk, miso (if using), 1 teaspoon sea salt, lemon juice and black pepper. Blend until completely smooth and creamy. Taste for more salt and/or nutritional yeast. I personally add an extra 1/2 teaspoon sea salt.
Chop broccoli florets into small 1/2” pieces (you can leave them larger, but I really love the texture of small broccoli pieces). Add broccoli, pasta, and as much “cheddar cheese” sauce as you like to the same 6 quart pot you’ve been using. Turn heat to low and cook, stirring, until pasta is warmed through. Serve! Pasta will keep for up to 5 days in the refrigerator or 2 months frozen.