Add olive oil, onion, and garlic to large pot and cook over medium-low heat, about 3 minutes.
Add kale and continue to cook for 1-2 minutes. Add spinach, broth, water, and salt and pepper to taste. Bring to a boil over high heat, then simmer over medium heat until spinach and kale are tender, about 10-15 minutes.
Ladle into bowls, garnish with Parmesan and serve with hunks of crusty baguette or other bread.