Blend cashews and 1 cup vegetable broth in a blender until smooth, about 1 minute.

Pour the remaining 4 cups vegetable broth into a large pot; add potatoes and onion. Bring to a simmer, cover, and cook for 5 minutes. Stir in broccoli and basil; return to a simmer. Cover and cook until potatoes are tender, about 10 minutes.

Stir cashew mixture into soup; add salt and black pepper. Bring to a simmer and immediately remove from heat. Transfer about half the soup to a blender; blend until smooth. Return blended soup to pot and stir well. Serve immediately.