In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the chicken pieces and season with salt and pepper. Cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.

In the same skillet, add the bell pepper, broccoli, snap peas, and carrots. Stir-fry the vegetables for about 3-4 minutes until they are tender-crisp.

Add the minced garlic and ginger to the vegetables and stir-fry for an additional 1 minute 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 and coats the chicken and vegetables.

Serve the stir-fry over cooked rice or noodles.