To make the pickled red onion, combine vinegar, sugar and salt in a small saucepan. Bring to the boil, stirring until sugar dissolves. Place onion in a heatproof bowl, pour over the hot pickling liquid. Stir to combine. Place in the fridge to cool.
To make the katsu sauce, combine all the ingredients in a small saucepan. Stir over medium heat until sauce just comes to the boil. Set aside to cool.
Carefully butterfly one chicken breast open, the cut down the centre to form two thinner fillets, repeat with remaining chicken. Place onto a piece baking paper on a board. Use a meat mallet flatten the chicken fillets to 1/2cm-thick.
Spoon flour and breadcrumbs onto separate plates. Whisk the eggs and 1 tablespoon cold water in a wide dish. Dip the chicken into the flour, then into the egg, then into the breadcrumbs, pressing crumbs on with fingertips.
Cover the base of a large frying pan with vegetable oil and heat over medium heat. Cook the chicken in batches, for 2-3 minutes each side or until golden and cooked through. Transfer to a board, cut into thick pieces.
Spoon rice into the base of 4 serving bowls. Arrange the chicken, lettuce, cucumber, avocado and pickled onion in the bowls. Drizzle over the katsu and mayonnaise. Serve.