Make a cut along the back of the prawns with a paring knife until you have cut almost, but not quite through, to the other side. Toss together the prawns, coriander, garlic and 1 teaspoon of the oil in a large bowl; put aside.
Heat the remaining oil in a large nonstick frying pan over moderate heat. Add the carrot and spring onions and cook for 2 minutes. Add the ginger and cook for 2 minutes. Cool the vegetable mixture to room temperature.
Preheat the griller. Place the prawns, cut-side-up, on the griller tray, pressing them down to flatten slightly. Spoon the vegetable mixture onto the prawns and grill 15 cm from the heat for 4 minutes or until the prawns are just cooked through.
Meanwhile, combine the soy sauce, chilli sauce and lime juice in a large bowl. Add the lettuce, cucumber and mint, tossing to combine. Serve the grilled prawns on a bed of the salad mixture.