Start by chopping your onion and mincing the garlic, setting them aside for later.
Heat two tablespoons of olive oil in a large heavy-bottomed pot over medium heat until shimmering and fragrant. Add the diced onion and cook, stirring occasionally, until translucent and soft, about 5 minutes. The kitchen should fill with a warm, savory aroma.
Add the minced garlic to the pot and cook for another minute until it becomes fragrant, stirring constantly to prevent burning.
Stir in the broccoli florets and cook for 5 minutes, allowing them to turn a brighter green and develop a nutty aroma.
Pour in the vegetable broth, then bring the mixture to a gentle boil. Reduce the heat and simmer, uncovered, for 10-12 minutes until the broccoli is tender but still vibrant.
While the soup simmers, drain and rinse your soaked cashews. Transfer them to a blender along with the nutritional yeast, smoked paprika, and a pinch of salt. Blend until smooth and creamy, about 2 minutes, adding a splash of broth if needed to help blending.
Carefully pour the hot soup into the blender containing the cashew mixture. Blend until completely smooth and velvety—this may take about 1-2 minutes. Be cautious when blending hot liquids; blend in batches if necessary.
Pour the blended soup back into the pot and warm over low heat. Stir constantly and taste—add salt or pepper as needed. Let it simmer gently for 5 minutes to meld the flavors and thicken slightly.
Once heated through and seasoned to your liking, serve the soup hot in bowls. Finish with a drizzle of olive oil or a sprinkle of fresh herbs if desired, and enjoy the cozy, cheesy aroma.
