For the cheese sauce: Place the potatoes and carrots in a medium pot and add water to cover. Bring to a boil over high heat, reduce the heat to medium, and simmer uncovered for 10 to 15 minutes, until fork-tender. Drain.
While the potatoes and carrots are simmering, add the nutritional yeast, oil, water, salt, and garlic into a high-speed blender and set aside.
Chop the onions, garlic, celery and broccoli for the soup and set aside. Tip: I like to use my food processor to this step, it cuts down on prep time.
When the simmering potatoes and carrots are fork-tender, drain them and add to the blender. Blend the cheese sauce until smooth.
For the soup: In a large pot, sauté the oil, onion, and garlic over medium heat, stirring frequently. Cook for about 3 to 5 minutes.
To the pot, add the celery and broccoli and sauté for a few minutes more – about 8 minutes. Now, add the broth and cayenne pepper, salt, and pepper. Cover and simmer over medium heat for about 10. Turn off the heat and let the soup sit for a few minutes.
Then add the cheese sauce into the soup and stir to combine. Adjust seasonings to taste if desired.
Ladle the soup into bowls and swirl cashew sour cream sauce into each bowl. Top with Pan-Fried Garlic Croutons, paprika, and chopped green onion, if desired.
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