Heat 2 tablespoons of olive oil in a large pot over medium-high heat. Add the pancetta or bacon, onions, carrots, celery, and rosemary. Cook for about 5 minutes, until softened and starting to brown, stirring occasionally.
Add the garlic and sauté until fragrant, about 30 seconds.
Add HALF of the drained and rinsed cannellini beans, crushed tomatoes, and the chicken stock.
Use a blender to puree the other half of the beans and add them back to the pot.
Bring the mixture to a boil. Turn the heat down to low, and add the rest of the beans and the pasta, as well as the 1 teaspoon of kosher salt and ¼ teaspoon of black pepper. Simmer, covered, until pasta is cooked al dente (about 10-12 minutes).
Stir in the remaining 2 tablespoons of olive oil. Season with salt and pepper to taste. Serve with freshly grated parmigiano cheese and a drizzle of extra virgin olive oil, if desired.
