Heat a large heavy based casserole pan over a high heat. Add the oil and when it’s hot add the pieces of beef shin. Fry the beef for 4 to 5 minutes on each side so it takes on a lovely dark caramelised colour.
Now add the rest of the base ingredients to the pan. Give everything a stir, pour over 1.5 litres of water or enough to cover all the ingredients, and bring the pan up to a simmer. Turn the heat down, cover with a lid and let the beef cook very gently for 3 hours.
When the beef is lovely and tender take the pan off the heat and use a slotted spoon to lift the beef out onto a plate. Pour the cooking liquid through a fine sieve into a clean bowl or jug.
While the beef is cooling, skim the excess fat off the top of the broth, then add the broth back to the pan. Set the pan back over the heat and bring it up to a simmer. Pull the beef shin into small shards and pieces, discarding any tougher membrane or pieces of fat.
When the soup is simmering, add the noodles to the pan then after a minute or so, the beef along with the rice wine vinegar, tamari, sesame oil, spring onions and toasted sesame seeds Cook for a further minute or two then take the pan off the heat. Roughly chop the coriander and stir this through.
Check the seasoning. You can adjust the balance with a splash of more vinegar or tamari sauce.
Ladle the broth into a bowl and serve, with extra chilli if you like and a spritz of lime juice.