Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the chicken pieces to the skillet and cook for about 5-7 minutes, or until browned and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the mixed vegetables and stir-fry for 3-4 minutes until they are tender-crisp.
Add the minced garlic and ginger to the vegetables and cook for an additional 1-2 minutes until fragrant.
In a small bowl, mix the soy sauce, cornstarch, and water until smooth. Pour this mixture over the vegetables and stir well to combine.
Return the cooked chicken to the skillet and add the sesame oil. Stir everything together and cook for another 2-3 minutes until the sauce thickens slightly.
Serve the stir-fry over cooked rice or noodles.