Cut the chicken into bite-sized pieces.
In a medium bowl, combine 1 tbsp soy sauce and 2 tbsp cornstarch.
Add the chicken pieces to the bowl.
Toss until the chicken is evenly coated.
Set the coated chicken aside while preparing the sauce.
In a separate bowl, combine the rice wine vinegar, soy sauce, white cooking wine, honey, cornstarch, olive oil, and brown sugar.
Whisk until the sauce is smooth and fully combined.
Heat the sesame oil and olive oil in a large skillet over medium-high heat.
Add the coated chicken to the skillet.
Cook until the chicken is browned on all sides.
Remove the chicken from the skillet and place it on a plate.
Add the sliced mushrooms, snow peas, and green bell pepper to the skillet.
Pour the prepared sauce over the vegetables.
Cook until the vegetables are tender but still slightly crisp.
Add the minced garlic and ginger paste to the skillet.
Stir well and sauté for approximately 30 seconds, or until fragrant.
Return the cooked chicken to the skillet.
Stir to combine the chicken, vegetables, and sauce.
Continue cooking for approximately 5 minutes, or until the chicken is fully cooked and the sauce has thickened.
Serve warm with white rice, if desired.
Garnish with chopped green onions before serving.