For the pasta dissolve the salt in 425ml/15floz water at 28C-30°C/82F-86F (the temperature is critical, use a thermometer to check this).
Add about two-thirds of the water to the flour and start kneading by hand or in a food processor fitted with a dough hook attachment.
Add almost all the remaining water and continue kneading for about 15 minutes to obtain a stiff, perfectly smooth dough - only add the last of the water if necessary. Cover the dough with a damp cloth and set aside to rest for at least two hours. (To test whether it is ready to use, press your thumb hard into the dough - the imprint should not start to spring back.).
Roll out 120g-150g/4½oz-5½oz pasta dough using a pasta machine. Transfer the dough to a work surface dusted with flour. Using your hands, stretch the dough until it almost doubles in length.
Divide the dough in two and place them side by side. Dust with flour, and then roll each piece up like a Swiss roll and slice finely.
For the soup place the crushed garlic, chilli, basil and olive oil into a bowl and leave to marinate. Meanwhile place the remaining ingredients into a large saucepan along with 200-225ml/7-8fl oz warm water. Add a pinch of salt and simmer for 45-50 minutes, or until the beans are cooked.
Remove the vegetables and guanciale from the stew. Set the meat aside, but blend the vegetables with a ladleful of the broth in a food processor until smooth. Return this purée to the soup and bring back to a simmer. Add salt and freshly ground black pepper to taste.
Bring a large pan of salted water to the boil, add the pasta and simmer for 3-4 minutes, then drain.
Heat a griddle pan until hot. Add the guanciale and sear on each side until charred. Remove from the pan and cut into chunks. Add the pasta for the soup and cook for a further minute.
To serve, place the guanciale into the centre of each bowl. Ladle the pasta and soup on top and drizzle with the reserved garlic, chilli and basil oil.