Add the onion and carrots to a large pot with a tablespoon or two of water. Sauté until slightly softened, about 2 minutes.
Add the potatoes, beans, broth, nutritional yeast, thyme and garlic powder to the pot and bring to a boil over high heat. Reduce heat and simmer until the potatoes are easily pierced with a fork, about 8 minutes. Then add the broccoli and simmer 5 more minutes.
Turn off the heat and using a slotted spoon, remove and set aside about 4 cups of the veggies. Then puree the remaining soup in the pot, using an immersion blender. Or you may transfer to a stand blender in batches, using caution when pureeing hot liquids. Return the reserved 4 cups of veggies to the pot, stir in the plant milk and taste for salt. I added 1/2 a teaspoon at this point, but salt to your taste. Then serve and enjoy.
I like this soup fairly chunky, but if you're serving picky eaters, you may puree the entire soup instead of reserving some chunkier veggies. You may use the reserved veggies to stir back into the pot, or use them to garnish each bowl of soup.If you're avoiding nuts, use soy or coconut milk instead of cashew milk. You may also use the canned coconut milk if you want an even richer and creamier finish, however, this will add more fat.I've kept the seasoning simple here to please some picky eaters, but if you wish to amp up the flavour, you may add some cumin, paprika, or even some cayenne to add a little heat.