Prepare the Ingredients: Thinly slice the chicken and yellow onion. Mince the garlic, grate the ginger (if using), and thinly slice the cabbage. Chop the green onions for garnish.
Cook the Chicken: Heat the olive oil in a large skillet or wok over medium-high heat. Add the sliced chicken and season with salt and black pepper. Cook for 4-5 minutes, stirring occasionally, until the chicken is golden brown and cooked through. Remove from the skillet and set aside.
Sauté the Onion and Garlic: In the same skillet, add the sliced yellow onion and garlic. Cook for 2-3 minutes, stirring frequently, until the onion is softened and fragrant.
Add the Cabbage: Add the sliced cabbage to the skillet. Stir well to combine with the onion and garlic, and cook for 4-5 minutes, stirring occasionally, until the cabbage is slightly softened but still crisp.
Mix the Sauce: In a small bowl, whisk together the soy sauce, sesame oil, rice vinegar, and grated ginger (if using). Pour the sauce over the cabbage mixture and stir well to coat evenly.
Combine and Heat: Return the cooked chicken to the skillet, tossing everything together to combine. Cook for an additional 2-3 minutes, letting the flavors meld together.
Garnish and Serve: Remove the skillet from heat and garnish the stir-fry with chopped green onions. Serve warm as is, or pair with steamed rice or noodles for a complete meal.