Add the onion, celery and carrots to a large pot with a tablespoon or two of water. Sauté over medium heat until softened, approx 5 minutes. Add more water if needed to prevent sticking.
Then add the cauliflower, both potatoes, broth, and all the seasoning to the pot. Bring to a boil over high heat, then reduce to medium low. Cook until the vegetables are soft, approx 8-10 minutes.
Meanwhile, in a separate pot or skillet, cover your broccoli with water and bring to a boil, then lower heat to simmer and cook until fork tender, approx 4-6 minutes. Drain and set aside.
While the soup and broccoli are cooking, add all the cheddar sauce ingredients to your blender. Blend until smooth and set aside.
Use an immersion blender to puree your pot of soup until smooth. Then stir in the cooked broccoli and the cheddar sauce and mix well. Enjoy.
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Notes
If you do not have a highspeed blender, soak your cashews in boiling hot water for 15-20 minutes and then drain. This will soften them, making them easier to blend.
Make sure there are no loose bits of cashews in the cheese sauce for the best texture. Process a little longer if needed to make it smooth.
Cook the broccoli separately. You may use a steamer, another pot, or a skillet, but separately is best. Once the soup is pureed, add the cooked broccoli florets to the pot.
Cut your broccoli into SMALL bite-size florets since these will remain whole, and not be pureed with the remaining ingredients.
Use a deep potto avoid splashes when hand-blending your soup with an immersion blender.
Leftovers will keep refrigerated for 3-4 days, or frozen airtight for 3-4 months.