In a large pot, heat the olive oil over medium heat. Add the chopped onions and sauté for about 4 -5 minutes until they become translucent.
Add the chopped carrots, garlic, *broccoli and potatoes to the pot and sauté for another 5 minutes. *(Note: If you want some whole broccoli florets in your soup then reserve 1/2 of the broccoli for this)
Pour in the vegetable broth and bring the mixture to a boil. Reduce the heat to a simmer and cook for about 15-20 minutes, or until the carrots and potatoes are tender.
While the vegetables are cooking, drain and rinse the soaked cashews.
Once the vegetables are tender, remove the pot from heat and use an immersion blender to puree the soup until smooth. Alternatively, carefully transfer the soup in batches to a blender and blend until smooth, then return it to the pot.
Return the pot to low heat and stir in the plant-based milk, nutritional yeast, lemon juice, and paprika. Cook for an additional 5 minutes, allowing the flavors to meld.
If you reserved 1/2 of the broccoli then stir in the chopped broccoli florets and cook for another 5-7 minutes, or until the broccoli is tender but still vibrant green.
Season the soup with salt and pepper to taste.