Begin cooking jasmine rice according to package directions (15 to 18 minutes). This runs in the background while you prep the chicken.
In a small bowl, whisk together soy sauce, honey, rice vinegar, sesame oil, minced garlic, and grated ginger. Divide in half and set one portion aside.
Add chicken pieces to a large bowl and pour half the marinade over them. Toss to coat and marinate for at least 15 minutes. While waiting, steam broccoli and prep remaining vegetables.
Sprinkle cornstarch over marinated chicken and toss until evenly coated.
Heat vegetable oil in a large skillet or wok over medium-high heat. Add chicken in a single layer and cook 5 to 7 minutes until golden brown and cooked through to 165 degrees F. Work in batches to avoid overcrowding. Let chicken sit undisturbed for the first 2 minutes to build a crust.
Pour reserved marinade over cooked chicken. Stir and cook 2 to 3 minutes until sauce thickens and coats the chicken. Add a splash of water if sauce thickens too much.
If desired, whisk together optional sauce ingredients in a small saucepan and simmer 2 to 3 minutes until slightly thickened.
Divide cooked rice among serving bowls. Top with sticky chicken, broccoli, carrots, cucumber, and edamame. Drizzle with extra sauce, garnish with green onions and toasted sesame seeds, and serve immediately.
Notes
Chicken thighs stay juicier than breasts and absorb the marinade more deeply. If using breasts, reduce cook time by 1 to 2 minutes.
For spicier bowls, add 1 to 2 teaspoons of sriracha to the marinade.
Start the rice first so everything finishes at the same time. Total active time is about 40 minutes.
Store components separately in airtight containers for up to 4 days. Freeze chicken and rice for up to 3 months.