Preheat an outdoor barbecue for medium heat; lightly oil the grate.
Cook the prawns on the hot barbecue until they are bright pink on the outside and the meat is no longer transparent in the centre, 5 to 10 minutes. Arrange the prawns on a serving platter.
Heat the oil in a frying pan over medium heat. Fry the garlic in the hot oil until brown, 7 to 10 minutes. Remove from heat and stir the lemon grass, chillies, shallot, lime leaves, fish sauce, lime juice and chilli paste into the garlic; toss to combine. Spoon the sauce over the prawns. Garnish with the mint to serve.