In a mixing bowl, combine the chicken pieces, salt, beaten egg, canola oil, and cornstarch; toss until the chicken is evenly coated.
Heat the vegetable oil and sesame oil together in a large skillet over medium-high heat.
Add the coated chicken to the hot skillet and cook until golden brown and cooked through, turning as needed, about 5–8 minutes depending on piece size; transfer to paper towels and set aside.
In the same skillet, add the trimmed green beans and sauté over medium-high heat for about 5 minutes.
Add the mushrooms to the skillet and continue cooking for another 5 minutes, until the beans and mushrooms are tender.
Stir in the minced garlic and ginger and cook until fragrant, about 30 seconds.
Pour in the soy sauce and balsamic vinegar and stir to coat the vegetables evenly.
Return the cooked chicken to the skillet and toss everything together so the chicken is coated with the sauce; heat briefly to combine.
Serve immediately, for example over rice if desired.
