Bring the water and sugar to the boil and reduce the heat. Reduce, uncovered, to a syrup-like consistency then leave to cool. Stir in the lime juice and fish sauce. Mix in the chilli, garlic and carrot.
Shortly before frying, dust the vegetable strips with a little flour.
Whisk the egg yolk and water in a bowl. Combine the flour and salt, add to the egg mixture and whisk well. Use the batter immediately. Preheat the oven to 60°C. Warm the platter.
Shallow fry: Fill the frying pan to a depth of approx. 3 cm with oil and heat to 180°C. Using a wooden skewer, dip the vegetables in the batter one at a time and drain off any excess. Fry the vegetables for approx. 1 1/2 mins. on each side until light brown and drain on paper towels. Keep the vegetables warm in the oven, leaving the oven door slightly ajar.
Serve the sweet chilli dip alongside.