1.Using a mandoline, V-slicer or wide vegetable peeler, thinly slice cucumber and carrot lengthways into long ribbons. Combine cucumber, carrot, chilli, sugar and vinegar in a medium bowl. Stand for 10 minutes or until vegetables have softened, turning every few minutes. Drain.
2.Meanwhile, pulse fish, paste, fish sauce, lime leaves, beans, egg and half the coriander in a food processor for 1 minute or until smooth. Using oiled hands, shape mixture into four 12cm patties.
3.Heat oil in a large frying pan over medium heat. Cook patties for 2 minutes each side or until cooked through. Drain on paper towel.
4.Add bread rolls, cut-side down, to same frying pan; cook for 1 minute or until lightly toasted.
5.Sandwich rolls with fish burgers, sweet chilli sauce, pickled vegetables and remaining coriander.
Fish patties can be prepared several hours ahead; store, covered, in the fridge until ready to cook. To use kaffir lime leaves, fold a leaf in half and cut out the tough centre vein. Kaffir lime leaves will keep in an airtight container in the fridge for two weeks or can be frozen for up to 1 month. Use straight from the freezer.