Heat a large heavy-bottomed pot over medium heat and add a tablespoon of olive oil. Once shimmering, add the chopped onion and sauté until translucent and fragrant, about 5 minutes.
Add the crushed garlic to the pot and cook for another minute, stirring until fragrant.
Stir in the broccoli florets and cook for 5 minutes, allowing their edges to soften slightly and release a fresh aroma.
Pour in the vegetable broth and bring the mixture to a gentle simmer. Cook until the broccoli is tender and bright green, about 10 minutes.
In a small bowl, whisk together the flour and plant-based milk until smooth, then slowly pour into the soup, stirring constantly with a whisk to prevent lumps.
Continue simmering for another 10 minutes, stirring occasionally, until the soup begins to thicken and the flavors meld.
Use an immersion blender to blend about half of the soup directly in the pot, creating a velvety, creamy texture while leaving some broccoli chunks intact for texture.
Stir in the nutritional yeast or vegan cheese shreds until melted and well incorporated, about 2 minutes.
Season with salt and pepper to taste, and add a dash of hot sauce if you like a little extra kick.
Remove from heat and let sit for a few minutes to allow the soup to thicken further. Serve hot, garnished with fresh herbs or a drizzle of olive oil if desired.