Prepare instant brown rice according to package directions.
Pour broth into a heavy medium saucepan, along with sugar, soy sauce and mirin. Bring to a boil; reduce heat to medium-low.
Add mushrooms to simmering broth.
Stir egg whites and whole egg in a small bowl until just mixed. Add chicken to the simmering broth. Gently pour in the egg mixture, without stirring. Spr When the egg starts to firm up, after about 3 minutes, stir it with chopsticks or a knife. (The chicken will be cooked by now.).
Add water chestnuts and heat.
Divide rice into 4 bowls.
Ladle chicken mixture into bowls.
Sprinkle with scallions and chili peppers.
We prefer our scallions raw, if you like them cooked -- add at the same time as the water chestnuts.