Start by finely chopping the onion and mincing the garlic. Set aside.
In a large heavy-bottomed pot, melt the vegan butter over medium heat until it sizzles gently. Add the chopped onion and minced garlic, cooking for about 3-4 minutes until fragrant and translucent, with the aroma filling the kitchen.
Add the broccoli florets to the pot, stirring well. Cook for another 5 minutes until the broccoli turns a vibrant green and just begins to soften, hearing a slight crackle as it cooks.
Pour in the vegetable broth and bring the mixture to a gentle simmer. Cover the pot and cook for 10 minutes, until the broccoli is tender when pierced with a fork but still bright and colorful.
Meanwhile, in a small bowl, whisk together the nutritional yeast, shredded vegan cheese, and lemon juice. This will create the cheesy flavor base for the soup.
Once the broccoli is tender, carefully transfer the mixture in batches to your blender. Blend each batch until smooth and creamy, about 30 seconds, then pour back into the pot.
Stir in the cheese mixture and the plant milk, warming the soup over low heat. Continue stirring until the cheese melts completely and the soup becomes velvety, about 5 minutes. Avoid boiling to keep it smooth.
Taste the soup and adjust with salt, pepper, or extra lemon juice for brightness. The final dish should smell cheesy and have a bright green hue with a silky texture.
Serve hot in bowls, garnished with a sprinkle of extra nutritional yeast or chopped herbs if desired. Enjoy the cozy, nourishing flavors!