Blend half the beans: Drain and rinse one can (15 oz) of cannellini beans. Add this along with 1 cup of vegetable broth to a blender and blend until smooth. Set aside.
Sauté the vegetables: Heat olive oil in a large pot over medium heat. Add the diced onion and carrots and cook until softened, about 5 minutes.
Add aromatics and spices: Stir in the minced garlic, rosemary, and thyme. Cook for an additional minute until fragrant.
Incorporate remaining ingredients: Pour in the remaining can of whole cannellini beans, the blended bean mixture, and the remaining 1 cup of vegetable broth. Season with salt and pepper.
Simmer and thicken: Bring the soup to a boil, then reduce heat and simmer for 30 minutes.
Add spinach: Stir in the fresh spinach and cook until wilted, about 2 minutes.
Serve and enjoy: Ladle the soup into bowls and top with grated Parmesan cheese, if desired.