Spicy Stir-Fried Sesame Chicken with Green Beans and Shiitake Mushrooms

Combine soy sauce, sherry, and water in medium bowl; add chicken and stir to break up clumps. Cover with plastic wrap and refrigerate for at least 20 minutes or up to 1 hour.

Mix sesame oil, cornstarch, flour, and sesame seeds in medium bowl until smooth. Drain chicken in strainer; press out excess liquid. Toss chicken in cornstarch/flour mixture until evenly coated.

Whisk chicken broth, soy, sherry, chili sauce, sugar, cornstarch, 2 teaspoons sesame seeds, 1 teaspoon sesame oil, and 1 teaspoon garlic in small bowl to combine; set aside. Combine remaining 2 teaspoons garlic, ginger, and 1 teaspoon peanut oil in small bowl; set aside.

Heat 2 teaspoons peanut oil in 12-inch nonstick skillet over high heat until smoking; add half of chicken to skillet in flat, even layer. Cook, without stirring, but gently separating pieces, until golden brown on first side, about 1 minute; turn chicken pieces and cook until lightly browned on second side, about 30 seconds. Transfer chicken to clean bowl. Repeat with additional 2 teaspoons peanut oil and remaining chicken.

Add 1 tablespoon peanut oil to now-empty skillet; heat until just smoking. Add green beans and cook, stirring occasionally, 1 minute; add mushrooms and stir-fry until mushrooms are lightly browned, about 3 minutes. Push vegetables to sides of skillet to clear center; add garlic and ginger to clearing and cook, mashing mixture with spoon, until fragrant, 30 to 45 seconds; stir mixture into beans and mushrooms. Continue to stir-fry until beans are tender-crisp, about 30 seconds longer; return chicken to skillet. Whisk sauce to recombine, then add to skillet; reduce heat to medium and cook, stirring constantly, until sauce is thickened and chicken is cooked through, about 30 seconds. Transfer to serving platter, drizzle with remaining teaspoon sesame oil, and sprinkle with remaining teaspoon sesame seeds. Serve immediately.