In a large bowl mix the cornstarch with 1 tablespoon soy sauce, then add the chicken and toss to combine and coat the chicken well. Marinate in the fridge for 30 minutes if you have the time.
In a small bowl or container, mix together the remaining 3 tablespoons soy sauce, sherry, sugar, chicken broth, balsamic vinegar, and sesame oil. Set aside.
Heat 2 tablespoons of the oil in a large skillet or wok over medium-high heat. Add the chicken and stir fry until the pieces turn white but are not all the way cooked through; about 2 minutes for breast meat, 4 minutes for thighs. Remove to a plate with a slotted spoon.
Heat the remaining tablespoon of oil in the same skillet over medium-high heat. Add the bell pepper and stir fry for 1 minute, then add about ⅔ of the scallions, the garlic, ginger, ½ cup peanuts, and the chili peppers or flakes and stir fry for another minute until you can smell the garlic and ginger. Add the chicken, stir fry for another minute, then re-stir the sauce to blend and add that to the pan. Cook, stirring frequently, for about 2 more minutes until the chicken is cooked through and the sauce has thickened.
Turn into a serving dish and sprinkle with the remaining scallions and additional peanuts. Serve over hot rice, if desired.
Notes
I like my Kung Pao chicken on the spicy side, hence the generous amount of dried red chilis or red chili flakes, but if your family is not a bring-on-the-heat family, start with a smaller amount, taste, and add more if you wish.
If you can't find mirin, sherry is an acceptable substitution, but it is made of grapes rather than rice, so it will add a different flavor.
Cooking the ingredients in batches allows them to cook more quickly and gives all of the components of this stir fry better color and texture.