Heat olive oil or vegan butter in a large pot over medium heat.
Stir in the onion and garlic, and cook for about 3 minutes until they smell delicious.
Add carrots, potatoes, and vegetable broth to the pot.
Let it simmer for 15 minutes, or until the vegetables are soft and tender.
Stir in broccoli florets and cook for another 5 minutes.
In a blender, combine soaked cashews, nutritional yeast, Dijon mustard, lemon juice, turmeric, smoked paprika, and plant milk.
Blend until completely smooth and creamy.
Pour the blended mixture into the pot and stir well.
Use an immersion blender for a creamy texture, or leave some chunks for a hearty soup.
Stir in vegan cheddar cheese (if using) and let it melt.
Season to taste with salt, black pepper, and a pinch of red pepper flakes.
Serve warm with crusty bread or croutons.