Rinse rice under cold water and drain. Bring 3 cups water and rice to the boil, lower heat, cover and simmer for 12 minutes until water is absorbed and rice is tender. Combine vinegar, sugar and salt, stir until sugar dissolves and pour over rice stirring well. Spoon rice into a shallow dish and refrigerate for 5 minutes to cool quickly.
Cover bamboo mat with plastic wrap and press a quarter of cooked rice in a layer over the mat leaving a 1cm space at the top end. Spread a little wasabi paste in a horizontal line along the middle of the rice. Arrange strips of capsicum and cucumber over wasabi line.
Mix mayonnaise and John West Tuna together and spoon mixture along the wasabi line. Place sesame seeds onto a tray.
Holding the edges of the plastic covered mat nearest to you, roll up tightly. Roll in sesame seeds and wrap in plastic wrap and refrigerate until required. Repeat with remaining ingredients. Cut into thin slices and serve with soy sauce.