Slice all the vegetables and chicken into uniform pieces for even cooking. Mince garlic and grate ginger, if using.
Heat oil in a large skillet or wok over medium-high heat. Add chicken strips and season with salt and pepper. Cook until the chicken is golden and cooked through, about 5–6 minutes. Remove from the pan and set aside.
In the same pan, add a little more oil if needed. Toss in the bell peppers, broccoli, carrots, and red onion. Stir-fry for 4–5 minutes until just tender but still crisp. Add garlic and ginger and cook for another 30 seconds.
Return the cooked chicken to the skillet. Pour in the sweet chili sauce and soy sauce. Toss everything together until well coated and heated through, about 2–3 minutes.
Serve hot over cooked rice or noodles. Garnish with sesame seeds and sliced green onions.