Let the beans soak overnight. Discard the soaking water and replace with fresh water to cover them well. Simmer in a large pot until nearly tender, about an hour.
While the beans are simmering, trim and cut up all the other vegetables into a small dice,
When the beans have cooked sufficiently, add the vegetables to the pot and enough water to cover them by a good 3cm/1 inch, along with a drizzle of olive oil and a good pinch of salt, and the Parmesan rind if using. Simmer gently for a good 45 minutes.
Take a ladleful or two of the soup and purée it in a blender. Add back to the pot, along with the pasta and, if things look too thick or dry, more water. Simmer for another 8-10 minutes, mixing from time to time to avoid scorching or sticking, until the pasta is done.
Let the soup rest for a few minutes, then mix in the pesto before serving.