In a large skillet or wok, heat the olive oil over medium-high heat until shimmering.
Add the sliced chicken breasts to the skillet and season with salt and pepper. Sauté for about 5-7 minutes, or until the chicken is cooked through and no longer pink. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and grated ginger, stirring quickly to prevent burning. Cook for about 30 seconds until fragrant.
Add the shredded cabbage, sliced red bell pepper, and julienned carrots to the skillet. Stir-fry for 5-6 minutes until the vegetables are tender but still crisp.
Return the cooked chicken to the skillet and pour in the soy sauce, sesame oil, and rice vinegar. Toss everything together until well-coated. Cook for an additional 2-3 minutes to heat through.
Remove from heat and sprinkle chopped green onions and sesame seeds on top for garnish.