As Tamar Adler says, "Parmesan rinds are definitively old." The rind is nothing but aged cheese and so when slowly stewed in water softens and lends a salty richness to any sort of broth, perfect for sopping up with thick slices of sourdough toast.
In a large soup pot, heat a glug of olive oil over medium heat and sweat the onions, carrot, and celery with a big pinch of salt until soft
Add the beans, cheese rinds, and herbs and 2 quarts of water and bring to a boil, reduce heat to a simmer and let cook until the beans are very tender and the cheese has started to render into the water
When the beans are done cooking add the thyme and garlic and let the beans rest overnight
Rewarm and serve with a big glug of olive oil over the top and served with a big piece of toast and green salad