Toss chicken with sherry and soy sauce in medium bowl; marinate until breast have absorbed flavors, about 10 minutes.
Mix garlic, ginger, and 1 teaspoon 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.
Heat 1 tablespoon oil in 10-inch skillet over high heat until just beginning to smoke.
Add chicken and cook without stirring for 1 1/2 to 2 minutes, allowing chicken to brown on one side; stir and cook 1 to 1 1/2 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.
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 15 to 20 seconds.