Heat 3 tbsp olive oil in a large heavy pot over medium heat. If using guanciale or pancetta, add it now and cook for 3-4 minutes, stirring, until the fat has rendered and the edges are lightly golden.

Add the diced onion and celery. Cook over medium-low heat for 8-10 minutes, stirring occasionally, until soft and pale gold but not browned.

Add the sliced garlic and chili flakes (if using). Cook for 1-2 minutes until fragrant.

Stir in the tomato paste and cook for 2 minutes, pressing it around the pot until it darkens slightly and smells sweet.

Add the drained soaked beans (or canned beans), warm broth, 400 ml water, the rosemary sprig, and the bay leaf. Stir to combine.

Bring to a gentle boil, then reduce heat to a steady simmer. Cook uncovered for 40-50 minutes for soaked dried beans (or 20 minutes for canned), until the beans are completely tender and the broth has thickened slightly. Add extra water if the level drops too low.

Remove the rosemary sprig and bay leaf. Using a wooden spoon or a fork, roughly mash about one quarter of the beans against the side of the pot to create a naturally thick, creamy base. Season with 1 tsp salt and taste - adjust as needed.

Bring the broth to a gentle simmer (not a rolling boil). Add the sagne pasta and stir immediately to prevent sticking.

Cook for the time indicated on the pasta package minus 1 minute, stirring every couple of minutes. The pasta should be just tender but still hold its shape - it will continue cooking as the soup rests.

Check consistency: the soup should be thick enough to coat a spoon. Add hot water in small amounts if it has thickened too much before the pasta is done.

Remove the pot from the heat. Add a generous grind of black pepper and stir once.

Let the soup rest off the heat for 5 minutes so the pasta absorbs the last of the broth and the flavors settle.

Ladle into deep bowls and finish each portion with a drizzle of raw extra virgin olive oil. Serve with toasted bread if you like.