Julienne the carrot into thin matchsticks and slice the onion thinly.
Combine the vinegar, soy sauce, sugar, water, and dashi granules in a small saucepan. Add the chilli if using. Bring to a simmer over medium heat, stirring until the sugar dissolves.
Season the fish lightly with salt. Cut into pieces if using larger fish, or leave whole for small fish. Coat with potato starch.
Heat a generous amount of oil in a frying pan over medium-high heat. Fry the fish pieces until golden and cooked through — about 3–4 minutes per side depending on thickness.
Transfer the hot fish to a container and pour the warm nanban sauce with the vegetables over the top. Make sure every piece is coated.
Marinate for at least 30 minutes — overnight is even better. Serve at room temperature or cold with plenty of the marinated vegetables.