Prepare the chicken. Slice the chicken against the grain into pieces approximately 1/4-inch thick. Transfer the chicken to a medium-sized mixing bowl and combine it with the cornstarch and soy sauce. Use your hands to coat the chicken pieces with a thin layer of the cornstarch mixture.
Mix the sauce. Add oyster sauce, rice vinegar, sesame oil, water, honey, and white pepper 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. Set the skillet over medium heat. Add the remaining tablespoon of oil. Once hot, add the shallots and sauté for 1 minute, stirring frequently. Add the minced garlic, ginger, and half of the green onions to the pan. Mix well to combine and sauté for 30 seconds, or until fragrant. Return the chicken to the skillet, mixing well to combine.
Add the sauce and bok choy. Give the sauce a final stir, then pour it directly into the skillet. Stir in the bok choy and continue to cook until the sauce has thickened, the chicken is cooked through, and the bok choy is softened. Garnish with the remaining green onions, if desired.