Toss the chicken with the egg white, 1 tablespoon each rice wine and cornstarch, 1 teaspoon soy sauce and 1/4 teaspoon salt in a medium bowl. Mix together 1/3 cup water, the remaining 4 teaspoons of soy sauce, 1 tablespoon rice wine and 2 teaspoons cornstarch, the sugar and 1/2 teaspoon each salt and pepper in a small bowl until dissolved; set aside.
Place the sauce, vegetables and chicken near the stove. Heat 2 tablespoons of the peanut oil in a large wok or large nonstick skillet over medium-high heat; swirl to coat the wok. Once the oil is hot, scoop the chicken from the bowl with a slotted spoon, letting any excess coating remain in the bowl, and add to the oil. Stir-fry, breaking the chicken up just enough so it doesn't clump, until the outside coating is set and lightly golden, 2 to 3 minutes. Remove the chicken with a slotted spoon and set aside. Wipe the wok out if needed.
Return the wok to medium-high heat and add the remaining 2 tablespoons of oil to the wok. Just as the oil begins to smoke, add the ginger and stir-fry until fragrant, about 30 seconds. Add the scallion whites and peppers and stir-fry until crisp-tender, about 3 minutes. Add the corn and stir-fry until just soft, about 1 minute. Add the chicken and the sauce (stir the sauce before adding); stir until the sauce is thick and the vegetables and chicken are cooked through, 1 to 2 minutes. Add the scallion greens. Serve with the brown rice.
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