Prepare the chicken- Slice the chicken against the grain into pieces approximately 1/4-inch thick. Transfer to a medium-sized mixing bowl and combine with the oil, cornstarch, and salt. Use your hands to coat the entire surface of the chicken with a thin layer of cornstarch.
Mix the sauce- Add all ingredients for the sauce (sesame oil, low-sodium chicken broth, soy sauce, oyster sauce, Shaoxing wine, and cornstarch) to a small mixing bowl. Whisk well to combine. Set aside.
Cook the chicken- heat a large, heavy-bottomed skillet over medium-high heat. Add 1 tablespoon of oil. Once the oil is hot, add the chicken pieces in a single layer and cook for approximately 30 seconds, or until the bottom is golden. Carefully flip each piece of chicken over and cook the other side for an additional 20-30 seconds. Immediately remove to a clean plate (the chicken will still be raw in the middle- that’s ok).
Sauté the aromatics- return the skillet to medium heat. Add the remaining tablespoon of oil. Once hot, add the minced garlic and half of the green onions to the pan. Mix to combine and sauté for 30 seconds, or until fragrant.
Cook the remaining vegetables- Add the carrots and mushrooms to the skillet, mixing well to combine. Cook, stirring often until the vegetables start to turn soft, approximately 3 minutes. Add the snow peas, bamboo shoots, and water chestnuts, mixing well to combine. Continue to cook for an additional 2 minutes or so.
Add the sauce and return the chicken. Give the sauce a final stir to dissolve the cornstarch and pour directly into the skillet with the vegetables. Add back the chicken and the remaining half of the green onions. Mix well to combine and continue to cook until the sauce has thickened and the chicken is cooked through.
Serve immediately with a side of rice and a sprinkle of sesame seeds, if desired.