In a medium bowl, combine the corn starch with cold water, whisking until smooth. Blend in chicken broth, soy sauce, honey, toasted sesame oil, and red pepper flakes until thoroughly incorporated; set aside. Warm one tablespoon of olive oil in a spacious skillet or wok over medium-high heat. Introduce the chicken, seasoning with salt and pepper, and sauté for 3 to 5 minutes until fully cooked through; transfer from the pan. Lower the heat to medium and pour in the remaining olive oil. Add broccoli, both bell peppers, and carrots, stirring intermittently until vegetables are crisp yet tender. Stir in ginger and garlic and cook for another minute. Return the chicken to the skillet, mixing to combine. Re-whisk the reserved sauce and drizzle it over the chicken and vegetables, gently stirring to coat everything evenly. Bring the mixture to a boil, stirring as needed, and allow it to bubble for one minute. Serve immediately alongside rice or chow mein, if desired.