Heat oil: Heat 3 tablespoons olive oil in a large (10-inch) pot or Dutch oven over medium heat.
Cook pancetta: Add the pancetta 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 burn on one side.
Sauté vegetables: Add in the onion, carrots, celery, cook for 8 minutes. Stir with wooden spoon while it's cooking.
Add Garlic: Add in the minced garlic and stir, and cook for less than a minute (you don't want it to brown or burn).
Add broth + beans: Pour in the broth and the beans. Add in the bay leaf and rosemary sprigs. Raise the heat to high and bring to a boil. Reduce the heat and simmer, partially covered, for about 45 minutes. Check the seasoning while it's simmering and add a little salt, if needed, and some freshly ground black pepper, if you like.
Mash some of the beans: Remove the bay leaf and rosemary sprigs. You could either remove some soup (I added it to a serving bowl)leaving 2 cups soup in the pot and mash really well with a potato masher or a wooden spoon. I added back the unblended part to my mashed beans and stirred to combine. OR you could ladle out 2 cups of the soup and blend in a high-speed blender.
Combine the creamed soup: 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: Transfer to a serving bowl or ladle directly into soup bowls. Drizzle on some extra-virgin olive oil before serving. If you like, sprinkle on some Parmigiano-Reggiano cheese and crushed red pepper flakes. ENJOY!