To make the katsu sauce, combine all the ingredients in a small saucepan. Stir over medium heat for 4 minutes until sauce just comes to simmer, simmer for 2 minutes and set aside to cool.
Preheat oven to 200°C fan-forced. Combine the Broccolini® and carrots in a roasting pan, drizzle with oil and season. Roast for 15 minutes until vegetables are tender and light golden.
Meanwhile, spoon flour onto a plate. Whisk eggs and milk in a shallow dish. Combine the breadcrumbs and sesame seeds on a plate. Dip the beef into the flour, egg, then into the sesame crumbs. Pressing crumbs on with fingertips. Refrigerate for 30 minutes if time permits.
Cover the base of a large frying pan with vegetable oil and heat over medium heat. Cook the beef for 1-2 minutes each side or until golden and cooked through.
Place beef onto a large plate or board, top with Broccolini® and carrots. Drizzle with katsu sauce and mayonnaise. Serve with rice.