In a large pot, heat olive oil, add onion, celery, carrot, and garlic. Sweat for about 5 minutes. Stir in the beans, add stock and tomatoes, bring to the boil, then reduce the heat and simmer for about 10 minutes.
Increase the heat, add the pasta, then reduce the heat to medium and cook until the pasta is ready. Remove from the heat, stir in the Parmigiano Reggiano rinds and leave to rest for 5 minutes. Season with salt and pepper as required.
In the meantime, combine the crispy bread, thyme leaves and a drizzle of olive oil. Divide the pasta & fagioli between bowls, sprinkle with the crispy bread mixture and serve.