Add the cashews to a small saucepan and cover with water by about one inch. Bring to a boil and cook for 8 minutes. Drain and set aside.
Set a soup pot over medium heat and add the butter. Once melted, add the onion and cook for about 3 minutes, until lightly browned.
Add the drained cashews, potatoes, broccoli, and broth to the pot. Bring just to a simmer. Do not boil. Cover and cook for 10 minutes, until the vegetables are tender. Remove from heat.
Stir in the Pesto.
Transfer the soup to a high-speed blender and blend until smooth. Blend in batches if needed. Alternatively, an immersion blender can be used directly in the pot.
Return the soup to the pot and gently stir in the parmesan cheese. Season with kosher salt and black pepper to taste.
Serve. Ladle into bowls, top with additional parmesan if desired, and serve warm.