Roughly chop the onion, carrot and celery. Place them in a food processor and pulse until very finely minced. You can also mince them by hand but they need to be very finely minced in order to meld into the stock.
Place the oil in a large pot over medium-low heat and add the two whole cloves of garlic. Gently fry for 2 minutes until beginning to soften but not brown.
Add the finely minced vegetables and gently sweat, stirring occasionally, until very soft - about 10 minutes.
Add the two cans of beans with the liquid from the can. The liquid helps thicken the soup but if it grosses you out you can rinse them first. Also add the crushed tomatoes and enough water to just cover - about 1 cup (250 ml).
Bring to a gently simmer and simmer for 15 minutes to reduce and bring out the flavour, stirring frequently so that the beans don’t stick to the bottom.
Remove the two garlic cloves. Transfer one ladleful (about 1/2 cup / 125 ml) of beans with a bit of the liquid from the pot to a food processor or the tall cup that comes with an immersion blender and blitz into a puree.
Add the bean puree back to the pot along with the pasta, salt, and enough water to cover and cook the pasta (about 2 cups / 500 ml).
Simmer until the pasta is al dente, stirring frequently so that it doesn’t stick to the bottom, and adding more water if necessary.
Optional: put the miso paste in a small bowl and spoon over a few tablespoons of the hot soup. Stir to dissolve the miso paste then add to the soup.
Adjust the consistency of the soup to your liking if you want it a bit thinner. I added another 1/2 cup (125 ml) of water. Italian pasta e fagioli should be quite thick, however, so don’t thin it too much. If it’s too thin, let it sit for a few minutes and it will thicken up.
Serve immediately before the pasta soaks up all the broth. Italian recipes usually add a drizzle of olive oil and lots of pepper over the bowl.