Heat the vegetable oil over a medium heat in a large soup pot. Add the garlic and ginger and fry for 5 minutes until soft. Add the leeks and fry for another 5 minutes.
Pour in the stock, soy sauce, mirin and sesame oil. Bring to a boil then drop in the nests of noodles and the carrot and stir through. Cook the noodles as long as it says on the packet, probably about 3-5 minutes.
Serve the soup topped with a boiled egg, some sliced radish, a sprinkling of sesame seeds and a slice of lime.