Cover your cashews in hot water and soak for 15 minutes for the cheddar sauce.
In a large pot or Dutch oven, saute the onion, garlic, celery, carrots and potatoes with about a tablespoon of water on medium high heat until the vegetables begin to get soft, about 8-10 minutes. Add water a little at a time if things begin to stick.
Add the broccoli florets and 5 cups of stock, and bring to a boil. Reduce the heat, and simmer until the vegetables are tender, about 10 minutes.
To Make the Cheddar Sauce. While the soup is simmering, drain the soaked cashews, and add them to a high speed blender. Add 1 cup of broth, the apple cider vinegar, nutritional yeast, tomato paste, Worcestershire sauce, Dijon mustard, garlic powder, onion powder, smoked paprika and optional cayenne pepper. Blend on high speed until smoth and creamy, stopping to scrape down the sides of the blender as needed.
When the vegetables are tender, add the cheddar sauce to the pot, and stir well.
Turn the heat off stove. Add soup to the blender in batches, and process until blended but still a little chunky--or to your desired consistency. (Or use an immersion blender ro blend in the pot.)
Return the blended soup to the pot and heat through, about 3-5 minutes.
To make the optional broccoli croutons: place a handful of reserved broccoli florets on a parchment paper lined baking sheet, and bake at 400 degrees Fahrenheit for about 10 minutes, or until just tender and lightly browned.
Cheese Sauce. This recipe makes a rich, cheddar-flavored soup. But you can use any vegan/compliant cheese sauce. For example, my Easy Cheezy Sauce is a simpler version, or my Chickpea Cheese Sauce is a high fiber, low fat version.
Broccoli. To maximize nutrition, chop 45 minutes or more before cooking. See this video for details.