Put the cashews and 1 cup of the vegetable stock into a blender. Blend until smooth, about 1 minute.
Put the remaining 4 cups vegetable stock, the potatoes and the onion into a large pot. Bring to a simmer, cover and cook for 5 minutes. Stir in the broccoli and basil and return to a simmer. Cover and cook until the potatoes are tender, about 10 minutes.
Stir in the cashew mixture, the salt, the pepper and bring just to a simmer. Remove from the heat, transfer about half of the soup to a blender and puree, or use stick blender. Return the puree to the pot and stir well. Serve immediately.