Start by patting your fish fillets dry with a paper towel, then cut them into small pieces.
In a food processor, blend the fish pieces, red curry paste, beaten egg, fish sauce, and sugar until you get a smooth paste.
Transfer the fish mixture to a bowl, then fold in the chopped long beans and Thai basil. Mix until everything is well combined.
Heat vegetable oil in a frying pan over medium-high heat.
Form the fish mixture into small patties (around 1 to 1.5 inches in diameter) with your hands. Be sure to make them compact so they hold their shape while frying.
Once the oil is hot, gently slide the patties into the pan. Fry them until they're golden brown and crispy on both sides. This should take about 2-3 minutes per side.
Use a slotted spoon to remove the fish cakes from the oil and drain them on paper towels.