place the rice in a large sieve. Rinse under cold running water, stirring occasionally to remove any excess starch, until the water runs clear. Drain.
combine the rice and water in a medium saucepan over high heat. Cover and bring to the boil. Reduce heat to low and cook, covered, for 12 minutes or until water has absorbed. Set aside, covered, to cool slightly.
meanwhile, combine the mayonnaise and eggs in a bowl. Use a fork to mash until smooth.
combine the cucumber, carrot and hoisin sauce in a bowl.
place 1 nori sheet, shiny-side down, on a sushi mat. Use wet hands to spread one-quarter of the rice over the nori sheet, leaving a 2cm border at 1 short end.
spread one-quarter of the egg mixture over the rice. Top with one-quarter of the cucumber mixture. Top with avocado slices. Roll sushi mat up firmly to enclose the filling. Repeat to make 3 more rolls.
cut the sushi rolls into 1.5cm slices. Serve with soy sauce.