In a medium bowl, mix the corn starch with cold water until fully dissolved. Incorporate the chicken broth, soy sauce, honey, sesame oil, and red pepper flakes, whisking until the sauce is smooth and well combined. Set aside.
In a large skillet or wok, heat one tablespoon of olive oil over medium-high heat. Add the chicken pieces, season them with salt and pepper, and cook for 3 to 5 minutes until they are no longer pink inside. If needed, cook in batches to avoid overcrowding the pan. Once done, remove the chicken and set it aside.
Lower the heat to medium and pour in the remaining tablespoon of olive oil. Add the broccoli, bell peppers, and carrots to the skillet, stirring occasionally, until the vegetables are just tender yet still crisp. Toss in the minced ginger and garlic, cooking for another minute until fragrant.
Return the cooked chicken to the skillet, stirring everything together. Give the stir fry sauce another whisk and pour it over the chicken and vegetables. Stir gently to coat the ingredients evenly. Raise the heat slightly, bringing the sauce to a boil, and let it bubble for about a minute, stirring occasionally until it thickens.
Serve the chicken stir fry hot, optionally paired with rice or chow mein noodles.