Combine soy sauce, sesame oil, corn-starch, sugar, a pinch of salt, and pepper in a small bowl. Set aside the sauce.
Heat vegetable oil in a large pan or wok over medium-high heat.
Sauté minced garlic and grated ginger for about 30 seconds until they become fragrant.
Add the chicken strips and cook for 4-5 minutes until they turn brown and are no longer pink.
Add the broccoli florets and sliced red bell pepper to the pan. Stir-fry for an additional 3-4 minutes until the vegetables become tender-crisp.
Pour the sauce over the chicken and vegetables in the pan. Stir thoroughly to coat everything evenly. Cook for another 2-3 minutes until the sauce thickens and coats the ingredients.
Taste and adjust the seasoning with more salt and pepper if necessary.
Serve the hot chicken stir-fry over cooked rice or noodles.