1. Toss chicken with sherry and soy sauce in medium bowl; marinate until breasts have absorbed flavors, about 10 minutes. Mix garlic, ginger, and 1 tablespoon oil in small bowl; set aside. Combine peanuts and chiles in small bowl; set aside. Mix chicken broth, vinegar, sesame oil, oyster-flavored sauce, hoisin sauce, and cornstarch in small bowl or measuring cup; set aside.

2. Heat 1 tablespoon oil in 12-inch skillet (cast iron is preferred) over high heat until just beginning to smoke. Add chicken and cook without stirring for 2 minutes, allowing chicken to brown on one side; stir and cook 1 1/2 to 2 minutes more, until no longer pink; stir peanuts and chiles into chicken and continue cooking until peanuts have darkened slightly, 30 to 40 seconds longer. Transfer chicken, peanuts, and chiles to bowl; set aside.

3. Return skillet to burner and reheat briefly, 15 to 30 seconds. Add remaining 1 tablespoon oil, swirl to coat pan, and add red bell pepper; cook, stirring occasionally, until slightly softened, about 45 seconds. Clear center of pan, add garlic-ginger mixture, mash into pan with spoon or spatula, and cook until fragrant, 10 to 15 seconds; stir into peppers until combined. Stir broth mixture to recombine, then add to skillet along with reserved chicken, peanuts, and chiles; cook, stirring and scraping up browned bits on bottom of pan, until sauce has thickened to syrupy consistency, about 45 seconds. Stir in scallions and serve.