Drain the soaked cashews and transfer them to a blender. Add nutritional yeast, smoked paprika, and 1/2 cup of water or plant-based milk. Blend until completely smooth and creamy, checking for a velvety texture with no grit.
Heat olive oil in a large pot over medium heat. Add diced onion and sauté until fragrant and translucent, about 5 minutes, until it begins to turn golden.
Add minced garlic to the pot and cook for about 30 seconds, until fragrant and just starting to brown, stirring constantly to prevent burning.
Stir in the chopped broccoli and cook for 2 minutes, allowing it to become slightly tender and vibrant green, releasing a fresh aroma.
Pour in the vegetable broth, bringing the mixture to a gentle boil. Reduce heat to low and simmer until broccoli is tender, about 8 minutes, until you can pierce it easily with a fork and it remains bright green.
Use an immersion blender directly in the pot, or carefully transfer the hot mixture to a blender in batches. Blend until smooth and creamy, with a silky, thick consistency, then return it to the pot if needed.
Stir in the prepared cashew cheese mixture, mixing well to incorporate. Heat gently for another 2-3 minutes, stirring often, until the soup is hot and fragrant, with a cheesy aroma.
Taste the soup and adjust seasoning with salt and pepper. If desired, add a few drops of liquid smoke for extra smoky flavor, tasting as you go to prevent overpowering.
Serve the soup hot, garnished with an extra sprinkle of nutritional yeast or chopped herbs if you like. Enjoy its velvety, cheesy richness with a vibrant green hue in every spoonful.
