Heat the oven to 375°F (170°C). Heat the oil in an ovenproof pan with a tight-fitting lid over a medium heat. Add the ribs and brown all over, then remove from the heat and arrange so the bones face down in the pan.
Stir together the tamari, mirin, sesame oil, gochujang, garlic and ginger, then spoon over the meat. Add the onion and pour 300ml of the stock around the ribs, without washing off the sauce. Add the lid and place in the oven for 2 and a half hours, basting with the sauce after 1 and a half hours and adding 100ml stock if needed (the sauce should be reduced and sticky by now). Cover again and return to the oven for the final hour until the meat is shreddable (if it’s not, return to the oven for 30 minutes with another splash of stock). Set aside until cool enough to handle, then transfer the meat to a plate.
Discard the excess oil from inside the pan, keeping 1 tbsp aside, leaving the sticky-sweet sauce and soft onions. Pull the meat from the bones and shred into pieces. Return the meat to the pan and discard the bones. (If the meat and sauce are now cold, warm gently over a low heat.)
Add the remaining ingredients, apart from the kimchi, to the cooked noodles. Add the reserved spiced oil from the pan and toss. Divide among 4 plates, top with the shredded beef and spoon over some of the sticky sauce from the pan. Serve the chopped kimchi in a little bowl on the table so your guests can decide if they want to try it – its hot sourness cuts brilliantly through the rich, sweet, spicy beef.