
Heat the olive oil in a large pot over medium-high heat. Add the onion, celery, and carrots. Season with salt and pepper and cook, stirring occasionally, until vegetables soften, about 10 minutes.
Stir in the zucchini, green beans, thyme, oregano, bay leaves, and garlic. Cook until fragrant, about 1 minute.
Add the tomato paste, crushed tomatoes with their juices, vegetable broth, and the parmesan rind if using. Bring the mixture to a boil, then reduce heat and simmer until vegetables are tender, about 20 minutes.
Stir in the kidney beans, white beans, and pasta. Simmer until pasta is al dente, about 8 minutes or according to package instructions.
Remove the bay leaves and parmesan rind before serving.
Ladle into bowls and top with freshly grated parmesan cheese and olive oil.