In a large pot on medium heat, add the onion and garlic and cook 3-4 minutes, until softened.
Add the carrots, potato, broccoli, broth and milk. Bring to a simmer, then cook about 5 minutes, until broccoli is bright green and fork-tender.
Using a slotted spoon or pair of tongs, remove large broccoli florets from soup and set aside.
Continue simmering soup about 10-15 minutes, until potato and carrot is fork-tender.
Transfer to a blender or use an immersion blender to blend until smooth.
Transfer soup back to pot. Add nutritional yeast, vegan cheese, reserved broccoli and lemon juice. Season with a pinch of salt and pepper. Taste and add more if necessary.
Stir until cheese is melted. Serve with fresh herbs, if desired.
