In a small heatproof bowl, cover mushrooms with boiling water, stand 20 minutes; drain. Discard stems; slice caps thinly.

Meanwhile, in a small jug, combine dashi with boiling water.

In a heated lightly oiled large frying pan, cook brown onion, stirring, about 10 minutes or until onion is browned lightly. Add half of the dashi mixture, reduce heat; simmer, stirring occasionally, about 10 minutes or until softened. Transfer to medium bowl.

In a large saucepan, bring rice and cold water to a boil, uncovered, stirring occasionally. Reduce heat to as low as possible; cover with a tight-fitting lid, cook rice 12 minutes. Do not remove lid or stir rice during cooking time. Remove from heat; stand, covered, 10 minutes.

Meanwhile, in same frying pan, combine remaining dashi mixture with sauce, mirin and sugar; bring to a boil. Add chicken and mushroom; cook, covered, about 5 minutes or until chicken is cooked through.

Combine egg with cooked onion in bowl, pour over chicken mixture; cook, covered, over low heat, about 5 minutes or until egg just sets.

Divide rice among serving bowls; top with chicken mixture, sprinkle with green onion.