In a large pot, heat up the extra-virgin olive oil and saute the garlic, onion, carrot, celery, and pancetta for 5 minutes. Add the fresh sage and rosemary, allowing the olive oil to absorb the flavors of the herbs. Season with salt and pepper to taste.
Add the beans and cook for a few minutes. With the back of a fork, mash up a quarter of the beans and add 1 cup water. Break the uncooked spaghetti into thirds using your hands and add into pot. Stir for about a minute. Add the remaining 3 1/2 cups water and bring to a boil. Cook for about 15 minutes, allowing the water to reduce until it becomes a thick consistency.
Let rest for 10 minutes off the heat. Add the freshly grated Parmigiano cheese, parsley, and finish with a drizzle of extra-virgin olive oil. Serve warm.