Chop up your onion and sautee in avocado oil with the minced garlic cloves. After a minute or so stir in your chopped veggies - butternut squash (keep the skin on!), peeled carrots, and celery stalks.
Stir in the vegetable broth, nutritional yeast, sea salt, paprika, garlic powder, and black pepper. Cook covered on a medium heat for about 20 minutes or until the vegetables are fork tender.
While the soup cooks, prep your broccoli. Add the broccoli heads to a food processor and quickly pulse a few times.
When the soup is done, let cool completely then blend in a high speed blender until smooth. Return back to your pot and mix in the pulsed broccoli. Let cook on a low/medium heat for about 10-15 minutes.
Depending on the size of your butternut squash, you may find the soup isn't creamy enough for you. If this is the case, sift in about 2 tbsp of corn starch. Sift it in gradually while stirring to avoid clumps. Also, keep in mind this soup firms up a bit in the fridge if you're meal prepping.
Lastly, stir in the vegan shredded cheese. Serve and enjoy, or keep in an airtight container for up to a week.