Begin by melting the vegan butter or heating olive oil in your large pot over medium heat. Add the diced onion and sauté until translucent and fragrant, about 3-5 minutes, until it begins to soften and smell sweet.
Add the minced garlic to the pot and cook for another minute, stirring constantly, until the garlic is fragrant but not browned—about 1 minute.
Stir in the broccoli florets, cooking for 2-3 minutes until they turn a brighter green and release a fresh aroma.
Pour in the plant-based milk and bring the mixture to a gentle simmer. Cover and cook for 8-10 minutes until the broccoli is tender but still vibrant.
While the soup simmers, add the drained cashews, nutritional yeast, smoked paprika (if using), and a pinch of salt and pepper to a blender. Blend until completely smooth, adding a splash of plant milk if needed to loosen the mixture.
Once the broccoli is tender, turn off the heat. Carefully transfer the soup to a blender or use an immersion blender directly in the pot. Puree until silky smooth, about 1-2 minutes, then return the soup to low heat.
Stir in the shredded vegan cheese, letting it melt into the warm soup, about 2-3 minutes, until the mixture is creamy and gooey.
Taste the soup and adjust the seasoning with additional salt, pepper, or nutritional yeast as needed. If the soup feels too thick, add a splash more plant milk and stir to loosen.
Remove from heat, let it sit for a minute to settle, then ladle into bowls. Garnish with extra broccoli florets or a sprinkle of vegan cheese if desired.
