Since the chicken needs to marinate for 15 minutes, get that started first. In a medium bowl, whisk together the soy sauce, dry sherry, and cornstarch until the cornstarch is dissolved. Add the chicken and toss to coat. Let stand at room temperature for 15 minutes, stirring occasionally.
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Meanwhile, chop the bell pepper, celery, scallions, and garlic.
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In another medium bowl, prepare the sauce by whisking together all of the sauce ingredients: balsamic vinegar, soy sauce, hoisin sauce, sesame oil, sugar, cornstarch, red pepper flakes, ground ginger, and water.
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Heat a large nonstick skillet over high heat until very hot. Add 1 tablespoon of the oil and swirl to coat. Add the bell pepper, celery, and salt.
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Cook, stirring frequently, until slightly softened and starting to brown, about 5 minutes. Transfer the vegetables to a large bowl and set aside.
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Add an additional 1/2 tablespoon of oil to the pan and set over high heat. Add half of the chicken (it’s important not to crowd the pan) and brown on one side, about 1-1/2 minutes.
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Turn the chicken pieces and continue cooking for about 1-1/2 minutes more, or until the chicken is just cooked through. Transfer the chicken to the bowl with the peppers and celery. Add another 1/2 tablespoon of oil to the pan. Add the remaining chicken and cook until golden on one side, about 1-1/2 minutes.
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Turn the chicken pieces over and cook for 1 minute. Add 1/2 tablespoon more oil to the pan, along with the garlic and scallions.
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Cook, stirring with the chicken, for about 30 seconds more.
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Add the reserved vegetables and reserved chicken to the pan, along with the sauce.
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Reduce the heat to low. Cook until the chicken and vegetables are warmed through and the sauce is thickened, about 30 seconds.
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Stir in the nuts. Taste and adjust seasoning, if necessary, and serve with rice.