Slice onion thinly. Cut chicken into bite-sized pieces, removing bones. Put soy sauce, sugar, mirin, sake, ginger juice and garlic in a pan. Add onion slices in the pot and simmer for a few minutes.
Boil enough water for 1/2 package of frozen carrots, broccoli and cauliflower. When water is at a boil, add contents of package of vegetables as well as 1/4 head of cabbage. When vegetables are almost done, (3-4 minutes), drain them. Add chicken and drained vegetables into the pan and simmer for a few minutes.
Serve hot steamed rice in a deep rice bowl. Put the chicken and vegetable topping on the top of rice. Place some beni shoga on the top if you would like.