In a large mixing bowl, combine the ground chicken, Thai red curry paste, egg, fish sauce, and sugar. Mix vigorously with a spoon or your hands until the mixture becomes slightly sticky and well incorporated, about 2 minutes.

Fold the finely chopped cilantro, sliced kaffir lime leaves (or lime zest), and sliced green beans into the chicken mixture. Stir gently until the herbs and vegetables are evenly distributed throughout the meat.

Wet your hands slightly with water to prevent sticking, then form the mixture into small patties, about 2 inches wide and 1/2 inch thick. You should get about 12 chicken cakes from the mixture.

Heat the vegetable oil in a large non-stick skillet over medium heat. Once the oil is shimmering, carefully add the chicken cakes in batches, making sure not to overcrowd the pan.

Fry the cakes for 3 to 4 minutes on each side, or until they are deeply golden brown and cooked through (the internal temperature should reach 165°F). Transfer the cooked cakes to a paper towel-lined plate to drain excess oil.

Arrange the warm chicken cakes on a serving platter and garnish with extra fresh cilantro if desired. Serve immediately with a small bowl of sweet chilli sauce for dipping.