Preheat oven to 350. Coat a 9 x 9-inch baking dish with cooking spray.
Place chicken in dish. Sprinkle onions all over. Combine soy sauce and next 5 ingredients (through garlic); pour over chicken.
Cover with foil and bake for about 30 minutes. Check for doneness.
Pour sauce in a small pot. In a small dish, mix the cornstarch with a little water to dissolve. If using flour, not necessary. Whisk it into the sauce. Bring heat up to a boil, turn down to low and simmer for a few minutes until the sauce thickens a bit. Pour sauce over chicken.
Add cabbage to a microwave-safe bowl and cook in the microwave for 2-3 minutes until soft.
To serve: Divide cabbage among 4 plates. Add 1 breast and spoon sauce over the top of chicken and cabbage. Sprinkle the top of each serving with ½ teaspoon sesame seeds and sliced scallions.
Makes 4 servings (each serving, 1 chicken breast, and sauce)