Heat 1 tablespoon of olive oil in a large skillet or wok over medium-high heat. Wait until the oil shimmers.
Add the sliced chicken to the skillet, stirring frequently until browned and cooked through, about 5-7 minutes. Ensure the chicken reaches an internal temperature of 165°F.
Once the chicken is cooked, remove it from the skillet and set aside. Add another tablespoon of olive oil if needed.
Add the minced garlic and ginger to the skillet, stirring quickly for about 30 seconds until fragrant.
Stir in the shredded cabbage, cooking for about 3-4 minutes until it softens but remains slightly crunchy.
Add the cooked chicken back to the skillet along with the soy sauce and sesame oil. Toss everything together for 1-2 minutes until heated through.
Season with black pepper to taste, and remove from heat. Serve immediately, garnished with green onions.