1. Prepare the Chicken: Start by cutting the chicken breasts or thighs into bite-sized pieces, about 1-inch cubes or thin strips. In a medium bowl, toss the chicken with 1 tablespoon of soy sauce and 1 tablespoon of cornstarch. This step helps tenderize the chicken and gives it a slight crispness when cooked. Set aside while you prepare the vegetables.

2. Chop the Vegetables: Wash and chop all your vegetables according to the ingredient list. Ensure your broccoli florets are small, carrots are thinly sliced, and bell pepper and onion are cut into similar-sized strips. Having all your vegetables ready before you start cooking is crucial for a stir-fry, as the cooking process is very fast.

3. Make the Stir-Fry Sauce: In a small bowl, whisk together the remaining 1 tablespoon of soy sauce, chicken broth, rice vinegar, and brown sugar (if using). If you want a slightly thicker sauce, you can add 1 teaspoon of cornstarch to this mixture and whisk until smooth. Set this sauce aside.

4. Cook the Chicken: Heat 1 tablespoon of vegetable oil and 1 teaspoon of sesame oil in a large skillet or wok over medium-high heat until shimmering. Add the marinated chicken in a single layer and cook for 3-4 minutes, stirring occasionally, until browned and mostly cooked through. Remove the chicken from the pan and set it aside on a clean plate.

5. Saute the Vegetables: Add the remaining 1 teaspoon of sesame oil to the same skillet. Add the broccoli and carrots first, as they take longer to cook. Stir-fry for 3-4 minutes until they start to become tender-crisp. Then, add the sliced red bell pepper, yellow onion, minced garlic, and grated ginger (if using). Continue to stir-fry for another 2-3 minutes until all vegetables are bright in color and tender-crisp, not mushy.

6. Combine and Finish: Return the cooked chicken to the skillet with the vegetables. Give the prepared stir-fry sauce a quick whisk again, then pour it over the chicken and vegetables. Stir everything together constantly for 1-2 minutes, allowing the sauce to thicken and coat all the ingredients evenly. The sauce should become glossy and cling to the food.

7. Serve Immediately: Remove the stir-fry from the heat and serve hot over freshly cooked rice or noodles. Garnish with a sprinkle of sesame seeds or chopped green onions if desired.