Start by making the vegan cheese sauce: Bring water to a boil in a medium saucepan. Add your diced potatoes and carrots (ideally chopped in a similar size), then reduce to medium heat and let it simmer, covered, for 10-15 minutes or until fork tender.
Add the remaining cheese sauce ingredients in a high-speed blender. Add the cooked potatoes and carrots and blend it all together until smooth. Set aside.
Heat oil in a large saucepan. Add the onion and garlic and cook until fragrant, about 5 minutes.
Add the broccoli, broth, nutritional yeast and salt. Bring to a boil, then reduce heat to low-medium and simmer for 5-10 minutes or until the broccoli is fork tender.
Transfer the soup to the blender, along with the cheese sauce. Blend it all together until smooth. Taste and adjust salt and add pepper to as needed.
Serve with roasted chickpeas or croutons if desired.