Step 1: In a medium bowl, combine the cubed chicken with 1 tablespoon of soy sauce and 1 teaspoon of cornstarch (if using). Toss to coat and set aside while you prepare other ingredients.
Step 2: In a small bowl, whisk together the remaining 2 tablespoons of soy sauce, chicken broth, oyster sauce, brown sugar, rice vinegar, and red pepper flakes (if using). Set aside.
Step 3: Heat 1 tablespoon of sesame oil in a large wok or skillet over high heat until shimmering. Add the chicken in a single layer and cook for 3-4 minutes, turning occasionally, until browned on all sides and cooked through. Remove the chicken from the pan and set aside.
Step 4: Add the remaining 1 tablespoon of sesame oil to the wok. Add broccoli florets, sliced bell peppers, and carrots. Stir-fry for 3-5 minutes, until vegetables are crisp-tender. Add snap peas, minced garlic, and grated ginger. Stir-fry for another 1-2 minutes until fragrant.
Step 5: Return the cooked chicken to the wok. Pour the prepared sauce over the chicken and vegetables. Stir constantly for 1-2 minutes, allowing the sauce to thicken and coat everything evenly.
Step 6: Remove from heat. Serve immediately over cooked rice or noodles. Garnish with chopped green onions and sesame seeds, if desired.