Heat oil: In a large (10-inch) pot or Dutch oven over medium heat heat 3 tablespoons olive oil .
Cook pancetta: Add the pancetta to the heated oil and and cook until it starts to crisp and the fat is rendered, about 4-5 minutes. Stir while it's cooking with wooden spoon so it doesn't brown too much on one side.
Sauté vegetables: Add in the onion, carrots, celery, and cook for 6-8 minutes, until softened. Stir with wooden spoon while it's cooking . Add the garlic in and stir for one minute, be sure to not let it brown.
Add in the tomatoes: and use a wooden spoon to break them up (if using canned plum tomatoes, break them up before adding, and remove the tough white core. Or puree' them in a blender, or use tomato passata).
Add broth + beans: Pour in the broth and half of the beans. Add in the bay leaf and rosemary sprigs. Bring to a boil with the heat on high. Lower the heat and simmer, partially covered, for about 45 minutes. Check the seasoning and add a little salt, if needed, and some freshly ground black pepper, if you like.
Blend the beans: Blend the other half of the beans in a blender. If it's hard to blend, add a little bit of broth. You could also mash them in a bowl with a fork or a potato masher.
Cook the pasta: in a separate medium sized pot in boiling and salted water until al dente. Drain, drizzle on olive oil and reserve in a bowl with a little olive oil drizzled on it until the soup is ready.
Combine the creamed beans: If you blended some of the soup, add it back to the pot and stir to combine. Add more broth if it's too thick and simmer to heat it before serving.
Serve: Ladle into soup bowls and drizzle a little bit of extra-virgin olive oil before serving. If you like, sprinkle on some Parmigiano-Reggiano cheese and crushed red pepper flakes. ENJOY!