In a large soup pot, heat olive oil and sauté the onion and garlic for 2-3 minutes over medium heat, stirring occasionally.
Add the potatoes, carrots, cashews, vegetable broth, nutritional yeast, smoked paprika, and salt.
Bring to a boil, then reduce heat and simmer for about 15 minutes until the vegetables are fork-tender.
Blend the soup in batches until smooth, then return it to the pot.
If the soup is too thick, add water to reach your desired consistency, about 1 cup.
Stir in the broccoli florets and cheese, if using, and simmer for 10 minutes until the broccoli is soft and the cheese has melted.
Serve with extra vegan cheddar cheese on top if desired.
Leftovers can be stored in an airtight container in the fridge for 3-4 days or frozen.