Sauté: In a large pot over medium heat, add a splash of water, diced onion, and garlic. Sauté for 5 minutes until the onion is soft.
Add carrots and celery, cooking for an additional 5 minutes until softened.
Season: Stir in thyme, paprika, and salt.
Cook: Add vegetable broth, nutritional yeast, diced potatoes, and cashew milk. Bring to a simmer, reduce heat to low, and cover. Let cook for about 20 minutes, or until potatoes are tender.
Blend: Remove from heat and allow the soup to cool slightly. Use an immersion blender or transfer in batches to a regular blender and blend until smooth.
Final Step: Return the blended soup to the pot, add chopped broccoli, and cook over medium-low heat for an additional 5-7 minutes until the broccoli is tender.
Serve: Serve warm and enjoy your delicious, dairy-free broccoli cheese soup!