Place the chicken pieces in a mixing bowl and add 1 teaspoon of the soy sauce and the cornstarch; toss to coat and marinate for 10 minutes.
Meanwhile, soak the dried red chiles in hot water for a few minutes until softened, then chop them; remove some seeds if you prefer less heat.
Heat a wok or large sauté pan over high heat. When very hot, add the canola oil and swirl to coat.
Add the marinated chicken in a single layer and sear, turning as needed, until lightly browned on all sides but not fully cooked, about 4 minutes.
Add the chopped chiles, minced garlic, diced red bell pepper, and chopped zucchini; stir-fry until the vegetables are fragrant and beginning to soften, about 1–2 minutes.
Stir in the remaining 1 teaspoon soy sauce, the chicken broth, and the balsamic vinegar; bring to a simmer, reduce heat to medium-low, and cook until the chicken is cooked through and the sauce slightly thickens, about 2 minutes.
Remove from heat, sprinkle with the chopped unsalted peanuts, and serve immediately.
