1. In a large, shallow bowl, whisk together soy sauce, 3 tablespoons water, vinegar, honey, garlic, and crushed red pepper.
2. Pour half of the mixture into another bowl; reserve.
3. Place chicken in remaining mixture;
4. marinate for 15 minutes.
5. In a 12-inch nonstick skillet, heat 1/2 tablespoon oil over high heat.
6. Add half the chicken; cook, tossing often, until brown and cooked through, 2 to 3 minutes.
7. Transfer chicken to a plate. Repeat with another 1/2 tablespoon oil and remaining chicken.
8. Wipe skillet with a paper towel.
9. Heat remaining tablespoon oil in skillet over medium-high heat.
10. Cook broccoli and lemon, tossing often, until broccoli is bright green, about 3 minutes.
11. Add 1/2 cup water; cook until broccoli is tender and lemon is translucent, about 6 minutes.
12. Add reserved marinade, cornstarch mixture, chicken, and any accumulated juices from plate.
13. Bring to a boil; cook, stirring until thickened, 1 minute.
14. Sprinkle with sesame seeds.