Peel and devein the shrimp, leaving the tails on. Trim the sharp tail tip. Make 3–4 shallow cuts on the belly to prevent curling.
Massage the shrimp with 1 tbsp potato starch and 1 tsp salt for 30 seconds. Rinse thoroughly under cold water and pat completely dry with paper towels.
For the tartar sauce: soak minced onion in cold water for 5 minutes, then drain and squeeze dry between paper towels. Chop the hard-boiled eggs and parsley finely. Mix all tartar ingredients in a bowl with Kewpie mayo, lemon juice, and salt to taste. Refrigerate.
Set up a breading station with flour, beaten egg, and panko. Coat each shrimp in flour (shake off excess), then dip in egg, then press firmly into panko.
Heat oil to 170–180°C (340–355°F). Fry shrimp for 2–3 minutes total, turning once, until deep golden brown. Drain on a wire rack.
Serve immediately with chilled tartar sauce, shredded cabbage, and a lemon wedge if you have one.