Heat a large heavy-bottomed pot over medium heat and add the olive oil, letting it warm until shimmering.
Add the chopped onion and sauté for about 3-4 minutes until it becomes translucent and fragrant, filling the kitchen with a sweet aroma.
Stir in the minced garlic and cook for another minute until it releases a fragrant, slightly nutty scent.
Add the broccoli florets to the pot and cook for about 5 minutes, stirring occasionally, until the broccoli turns a vibrant green and begins to soften.
Pour in the vegetable broth, bring the mixture to a gentle simmer, then cover the pot and let it cook for 8-10 minutes until the broccoli is tender but still bright.
Carefully transfer half of the soup to a blender and blend until smooth and creamy. Return the pureed soup to the pot, stirring to combine.
Stir in the plant-based milk, nutritional yeast, smoked paprika, and season with salt and pepper to taste. Warm gently for a few minutes until everything is well incorporated, avoiding boiling.
Taste the soup and adjust seasoning if needed, aiming for a cheesy, smoky flavor with a vibrant green hue.
Serve the soup hot, garnished with a sprinkle of nutritional yeast or fresh herbs if desired, and enjoy its comforting, creamy texture.