In a large 6-qt dutch oven over medium heat, sauté the diced onion in ½ cup of broth or water until it's soft and translucent. Add the garlic and cook for 1 minute. Add a little bit more liquid if it gets too dry. Next, add the potatoes, carrots, cashews, ½ tsp salt, and 3 cups of water to the pot. Bring it to a simmer and then reduce the heat to medium and cover it. Let it cook for 20 minutes or until everything is soft.
While the vegetables and cashews are cooking, prep the broccoli. If you use the whole broccoli crown, cut 1 ½ - 2 inches off the bottom of the stem (it's really tough and fibrous) and then dice the rest of the stem. You don't need to peel it first. Cut the florets into small, bite-sized pieces.
Let the veggie and cashew mixture cool a little bit before you transfer it to the blender. Depending on the size of your blender cup, you may need to work in batches if it isn't big enough.
Carefully transfer the cooked vegetable and cashew mixture to a large blender cup along with 1 cup almond milk, ½ cup nutritional yeast, 1 tbsp apple cider vinegar, 1 tsp paprika, ½ tsp turmeric, ¼ tsp chili pepper flakes, ½ tsp salt, and ½ tsp black pepper. Blend on high until it’s smooth and creamy.
Pour the puree back into the pot and stir in the remaining 3 cups of almond milk. Increase the heat to medium and bring the soup to a low simmer. Chop the broccoli into small pieces and put it into the pot. Let it cook for 10 minutes, stirring occasionally, or until the broccoli is tender but not mushy.
Finish with 2 tbsp of lemon juice and add more salt and pepper to taste. Add more broth or water if the soup is too thick.