Prep the Chicken and Veggies: Slice the chicken breasts thinly and set aside. Prepare the vegetables by cutting the broccoli into florets, slicing the bell pepper, and peeling and slicing the carrots. Mince the garlic and grate the ginger.
Cook the Chicken: Heat 1 tablespoon of olive oil in a large skillet or wok over medium-high heat. Add the chicken slices and cook for 5-7 minutes until fully cooked and lightly browned. Remove the chicken from the skillet and set aside.
Cook the Vegetables: In the same skillet, add the remaining tablespoon of olive oil. Toss in the broccoli, bell pepper, and carrots. Stir-fry for 4-5 minutes, allowing the veggies to become tender but still crisp. Add the garlic and ginger, cooking for another minute until fragrant.
Make the Sauce: In a small bowl, whisk together the soy sauce, oyster sauce (if using), rice vinegar, honey or maple syrup, cornstarch, water, and sesame oil (if using). Ensure the cornstarch is fully dissolved.
Combine Chicken, Veggies, and Sauce: Return the cooked chicken to the skillet with the vegetables. Pour the sauce over the mixture and stir well to coat everything evenly. Let it cook for 2-3 minutes, stirring frequently, until the sauce thickens.
Garnish and Serve: Sprinkle sesame seeds on top for garnish, if desired, and season with freshly ground black pepper to taste. Serve hot over steamed rice, noodles, or enjoy as-is for a low-carb option.