Sauté the vegetables: Heat olive oil in a large pot over medium heat. Add onion, carrots, celery, and garlic, cooking until softened (about 5 minutes).
Add greens and tomatoes: Stir in kale, cabbage, and diced tomatoes. Cook for another 5 minutes.
Simmer the soup: Add the beans, vegetable broth, thyme, oregano, salt, and pepper. Bring to a boil, then reduce heat and let simmer for 45 minutes.
Incorporate the bread: Stir in the stale bread and let it soak into the soup, thickening the texture.
Reboil the soup: Traditionally, Ribollita is left to cool and then reheated the next day for even better flavors.
Serve and enjoy: Drizzle with extra olive oil and sprinkle Parmesan cheese if desired. Serve warm.