Heat 2 tablespoons of olive oil in a large pot over medium heat. Add the onion, celery, and carrot. Cook for 7-8 minutes, stirring occasionally, until the vegetables are softened and fragrant.
Add the garlic and rosemary, then cook for about 30 seconds, just until fragrant. Pour in the white wine to deglaze the pot, scraping up any bits from the bottom. Let it simmer for 2-3 minutes, until mostly reduced.
Next, add the rinsed beans, a pinch of salt, and a few cracks of black pepper. Stir to combine. Note: for a slight creaminess to the soup, reserve about ¼ of the beans. After you add the broth in the next step, blend the reserved beans with 1-2 ladles of broth until smooth, then stir the mixture back into the pot.
Pour in the broth and stir. Add the parmesan rind (if using), then bring this to a bubble.
Reduce to a simmer, then add in the ditalini pasta and stir occasionally until the pasta is tender. Remove the parmesan rind at this point if you used one.
Ladle into bowls, and finish with some grated parmesan cheese and extra freshly cracked black pepper if you like.