Heat the olive oil in a large heavy-bottomed pot over medium heat until shimmering and fragrant.
Add the finely diced onion and minced garlic to the pot. Sauté, stirring occasionally, until the onion is translucent and fragrant, about 5 minutes. The mixture should smell warm and savory.
Stir in the broccoli florets, then pour in the vegetable broth. Bring the mixture to a gentle simmer, covering the pot, and cook until the broccoli is tender and vibrant green, about 10 minutes.
Remove the pot from heat and carefully blend the soup directly in the pot with an immersion blender until smooth and velvety. Alternatively, transfer the soup in batches to a blender, then return it to the pot.
Stir in the nutritional yeast, plant-based milk, lemon juice, and smoked paprika. Warm the soup over low heat, stirring gently, until everything is combined and heated through, about 3-5 minutes.
Taste the soup and season with salt and pepper as needed. If the soup is too thick, add a splash more plant milk or broth and stir to loosen. If it's too thin, simmer uncovered for a few more minutes to thicken slightly.
Once the soup is creamy, smooth, and hot, ladle it into bowls. Garnish with extra nutritional yeast or fresh herbs if desired. Serve immediately and enjoy that warm, cheesy aroma.