Place rice and 6 cups (1.5L) water in a large saucepan and bring to the boil. Reduce heat and simmer, covered, for 12 minutes or until water has absorbed and rice is tender. Set aside, covered, for 10 minutes to cool slightly.
Combine vinegar, sugar and salt in a small bowl and stir until sugar has dissolved. Transfer rice to a large glass or wooden bowl. Using a flat-edged spatula, break up lumps in rice while gradually adding vinegar mixture, gently folding to combine. Continue folding and fanning rice (use a hand-held fan or any similar object) for 15 minutes or until rice is cool.
Juice 1 lime. Combine juice, cucumber, fish sauce and soy sauce in a medium bowl. Set aside for 5 minutes to pickle. Drain.
Meanwhile, combine salmon with juice and zest of remaining lime in a chilled bowl. Add shallots and gently toss.
Place 1 cup sushi rice in each serving bowl and top with one-quarter each of the salmon mixture, avocado, seasonal vegetables and pickled cucumber. Drizzle with ponzu and sprinkle with black sesame seeds to serve.
NOTE: Ponzu is a tangy citrus-based sauce used in Japanese cooking and can be used as a dipping sauce or a dressing. It is available in the Asian food aisle of most supermarkets or from Asian grocery stores.
Before cooking, rinse the rice in a large sieve under cold water until the water runs clear. Drain well. This removes any excess starch, which can make the rice clumpy when cooked.
Serving Size 4