This recipe has much in common with donburi but, in Japan, would use a container called a kama, an earthenware pot. Typical Japanese fast food popular at railway stations, Kama-meshi from Yokokawa, Japan is regarded as some of the best.
Place skinned and boned chicken breast pieces into a glass bowl and pour the dark soy sauce and 2 tbsp sake over them. Mix by hand to ensure all pieces are coated with the liquid. Refrigerate until needed.
Rinse dried mushrooms well in cold water and rehydrate in hot water for 30 minutes. Drain and slice mushrooms thinly and add to a small saucepan. If using fresh, just rinse and slice but do not soak.
Combine both stocks and then add 1/2 cup of the combined stock to the small saucepan. Bring to a boil and add marinated chicken slices, the beef, and bamboo shoots. Stir and mix well, lower the heat to medium, cover the pan and simmer for three minutes.
Put the rice with the remaining stock, along with the salt, into a large saucepan or casserole dish with lid. Stir and bring this to a boil.
While boiling, add the light soy sauce, the rest of the sake and give the mixture another stir.
Add the beef and chicken mixture from the other pan. Do not stir this vigorously, but move the pieces around gently with a wooden spoon so the meat, bamboo shoots and mushrooms sit on top of the rice. The stock should be enough to cover the meat.
Cover the pan or casserole tightly and leave to cook undisturbed on medium heat for 20 minutes. Remove from heat, uncover briefly, and add the chopped scallions. Cover again, and leave the casserole to rest for 6 minutes. Serve immediately.