Heat a large pot over medium heat and add a tablespoon of olive oil. Once shimmering, add the chopped onion and cook, stirring often, until translucent and fragrant, about 5 minutes.
Add the minced garlic and cook for another minute until it releases a warm, aromatic smell.
Stir in the broccoli florets and cook for 3-4 minutes, watching for the bright green color to intensify and the broccoli to soften slightly.
Pour in the vegetable broth and bring the mixture to a gentle simmer. Cover the pot and let it cook for about 10 minutes, until the broccoli is tender and easily pierced with a fork.
While the soup simmers, blend the soaked cashews with water in a blender until completely smooth and creamy. This creates the rich base for the soup.
In a small saucepan, warm the nutritional yeast with a splash of plant milk over low heat, stirring until it forms a cheesy, velvety mixture.
Once the broccoli is tender, remove the pot from heat and use an immersion blender directly in the pot or carefully transfer the soup to a blender in batches. Blend until the soup is smooth, with some small chunks for texture if desired.
Stir in the cashew cream and the melted nutritional yeast mixture, then return the pot to low heat. Cook for another 5 minutes, stirring often, to allow flavors to meld. Season with salt, pepper, and a squeeze of lemon juice for brightness.
If the soup is too thick, add a splash more broth or plant milk and stir until smooth. If too thin, simmer uncovered for a few more minutes to thicken to your desired consistency.
Taste the soup and adjust seasonings as needed. The final result should be velvety, cheesy, and bright with the aroma of cooked broccoli.
Serve hot, garnished with a drizzle of olive oil or extra nutritional yeast if desired. Enjoy this comforting bowl of vegan broccoli cheddar soup!