To make dressing, whisk all ingredients in a small bowl until combined. Makes 180ml (3/4 cup).
To make omelettes, place eggs, fish sauce and 2 tablespoons cold water in a bowl, then whisk until combined.
Heat 1 tablespoon oil and 20g butter in a frying pan over medium–high heat. Add 6 prawns and one-quarter of the onion, and cook, tossing occasionally, for 2 1/2 minutes or until prawns are pink. Using a ladle, add one-quarter of the egg mixture. Season with salt and pepper. Cook for 5 minutes or until omelette is set and prawns are just cooked through. Transfer omelette to a plate and cover loosely with foil to keep warm. Repeat 3 more times with remaining oil, butter, prawns, onion and egg mixture.
Place carrot, spring onions, chillies and coriander in a bowl with half the dressing, and toss well to combine.
Divide omelettes among plates and top with salad mixture. Drizzle with remaining dressing to serve.