Heat a large pot over medium heat, then add a tablespoon of olive oil. Once shimmering, add diced onion and cook, stirring occasionally, until translucent and fragrant, about 5 minutes.
Add minced garlic to the pot and cook for another minute until it becomes fragrant, filling the kitchen with a warm aroma.
Stir in the broccoli florets and cook for 3 minutes, allowing them to turn bright green and slightly tender, making a satisfying crunch if tasted at this stage.
Pour in the vegetable broth and bring the mixture to a gentle simmer. Cook until the broccoli is soft and easily pierced with a fork, about 10 minutes.
Use an immersion blender directly in the pot, or transfer the soup in batches to a blender, and blend until smooth but still slightly textured. Be careful with the hot liquid!
Return the pureed soup to gentle heat, then stir in the plant-based shredded cheese, nutritional yeast, and plant milk. Keep stirring until the cheese melts into a creamy, cheesy consistency.
Season with salt, pepper, and a pinch of nutmeg, then simmer for another 5 minutes, tasting and adjusting seasoning as needed. The soup should be thick, creamy, and vibrant green.
Ladle the hot, cheesy broccoli soup into bowls, garnish with extra cheese or fresh herbs if desired, and serve immediately for a cozy, nourishing meal.