Step 1: In a medium bowl, combine the chicken pieces with 1 tablespoon of cornstarch and 1 tablespoon of soy sauce. Toss to coat evenly and set aside while you prepare the vegetables and sauce.
Step 2: In a separate small bowl, whisk together all the sauce ingredients: 1/4 cup soy sauce, honey/maple syrup, rice vinegar, sesame oil, 1 teaspoon cornstarch, and water/broth. Set aside.
Step 3: Heat 1 tablespoon of vegetable oil in a large wok or a heavy-bottomed skillet over high heat until shimmering. Add the chicken in a single layer (cook in batches if necessary to avoid overcrowding). Stir-fry for 3-5 minutes until browned and cooked through. Remove chicken from the wok and set aside.
Step 4: Add the remaining 1 tablespoon of vegetable oil to the wok. Add the broccoli florets and sliced carrots. Stir-fry for 3-4 minutes until slightly tender-crisp.
Step 5: Add the sliced red bell pepper and snap peas to the wok. Stir-fry for another 2-3 minutes until vegetables are tender-crisp. Add the minced garlic and grated ginger, and stir-fry for 30 seconds until fragrant.
Step 6: Return the cooked chicken to the wok with the vegetables. Give the prepared stir fry sauce a quick whisk (to ensure cornstarch is well mixed) and pour it over the chicken and vegetables.
Step 7: Stir constantly for 1-2 minutes, allowing the sauce to thicken and coat all the ingredients beautifully. The sauce will become glossy. Remove from heat immediately.
Step 8: Serve the stir fry hot over cooked rice, garnished with sesame seeds and sliced green onions if desired.