Combine half the cornstarch, half the soy sauce, dry sherry, rice wine vinegar and hot pepper sauce in a small bowl and stir with a whisk.
Combine remaining cornstarch, remaining soy sauce, and chicken in a medium bowl. Toss well to coat.
Heat a nonstick skillet over medium-high heat. Add cashews to the pan. Cook for 3 minutes or until lightly toasted, stirring frequently. Remove from the skillet.
In the same skillet, add extra-virgin olive oil and Brussels sprouts. Fry for 5 minutes or until lightly toasted, stirring frequently. Add water to the skillet until sprouts are just covered. Cook for 10 minutes and remove from the pan. Add dry garlic and salt to taste.
Add oil to the pan, swirling to coat. Add chicken mixture to the pan and fry for 2 minutes or until lightly browned. Remove chicken from the pan and place in a bowl.
Add bell pepper strips to the pan and fry for 2 minutes, stirring occasionally. Add garlic and ginger to taste. Cook 30 seconds.
Add cornstarch mixture and chicken to the pan. Cook for 1 minute or until sauce is slightly thick. Sprinkle with cashews and green onions.
Serve cashew chicken with Brussels sprouts and chopped green cabbage.