To make the broth, place the chicken carcass and wings in a large pan. Cover with cold water, then add the rest of the ingredients and simmer for 1 hr.
Strain the chicken broth into a clean pan. Carefully pick out any pieces of chicken and return to the broth. Put the broth back on the heat and bring back to the boil.
Add the noodles and cook for 3 mins until tender, then stir in the beansprouts, pak choi, red chili, soy sauce, honey and lime juice, adding the squeezed lime halves to the pot, too. Can be frozen at this point. Cook for 2 mins more. Ladle the soup into bowls, scatter over the spring onions and mint leaves, and serve with the lime wedges for squeezing over.