Pound the chicken breasts to an even thickness. Season both sides with salt and pepper.
Heat 1 tablespoon of olive oil in a skillet over medium-high heat. Add the chicken breasts and cook for about 5-6 minutes on each side or until fully cooked. Remove the chicken from the skillet and set it aside to rest.
In a pot of boiling water, cook the noodles according to package instructions. Drain and set aside.
In the same skillet used for the chicken, add the remaining olive oil. Sauté the minced garlic for a minute until fragrant.
Add the broccoli florets and sliced mushrooms. Cook for about 5-6 minutes until the vegetables are tender but still crisp.
In a bowl, whisk together the low-sodium soy sauce, rice vinegar, honey (or maple syrup), minced garlic, grated ginger, cornstarch, ground black pepper, and red pepper flakes (if using). Mix until the cornstarch is fully dissolved.
Heat a small saucepan over medium heat. Pour the mixture into the saucepan.
Bring the mixture to a simmer, stirring constantly. Allow it to cook for 2-3 minutes until the sauce thickens slightly. Stir continuously to prevent lumps.
If desired, add sesame oil for a nutty flavor. Stir it into the sauce and remove it from the heat.
Slice the cooked chicken breasts into strips and return them to the skillet with the sautéed vegetables.
Add the cooked whole wheat noodles to the skillet. Stir well to combine all the ingredients.
Pour the prepared Peppered Asian Sauce over the Peppered Chicken, Broccoli, Mushrooms, and Noodles in the skillet. Toss everything together until the sauce coats the ingredients evenly.
Garnish with sesame seeds.