Sauce: dissolve cornstarch in soy sauce. Add ginger, garlic, pepper, and sesame oil (optional) to cornstarch mixture and whisk to blend.
In saucepan, bring chicken broth and water to a boil.
Slowly add cornstarch mixture, whisking continuously until combined. Return sauce to a boil. Reduce heat to simmer and continue cooking until sauce is smooth and thick, about 3 to 5 minutes. Remove from heat.
In a medium skillet, heat 1 Tbsp oil over medium-high heat. Add chicken and saute over medium heat for 5 to 10 minutes until no signs of pink remain. Remove chicken and set aside.
In the same skillet, heat 1 Tbsp of oil over medium-high heat. Saute carrots for 4 minutes. Add onions and cook for 1 minute. Add broccoli and cook for 2 more minutes.
Add cooked chicken and reserved sauce to vegetables and toss to thoroughly coat.
