Bring a large saucepan of salted water to the boil and par-boil the noodles for 2-3 minutes. Drain and refresh in cold water, setting to one side.
Heat the sesame oil in a large wok over a moderate heat until hot. Stir-fry the broccoli, red onion and garlic for 2-3 minutes, stirring all the time. Drain the noodles really well and add to wok, stirring well. Add the coconut milk at this point and bring to a simmer for 2-3 minutes.
Season the stir-fry with the lime juice, soy sauce, then stir in the desiccated coconut. Remove from the heat and divide between 4 serving bowls. Sprinkle over the sesame seeds and garnish with the sliced red chilli. Serve with chopsticks.