Prepare all ingredients: thinly slice the chicken breasts, julienne the cabbage, mince the garlic and ginger, and measure out the sauce ingredients in a small bowl.
Heat your wok or large skillet over high heat until shimmering, creating a hot surface perfect for quick stir-frying.
Add a tablespoon of oil to the hot pan, swirling to coat. Once it starts to shimmer and faintly smoke, add the sliced chicken.
Stir-fry the chicken for 2-3 minutes, until it turns golden and is cooked through. Remove the chicken from the pan and set aside.
In the same pan, add a little more oil if necessary, then toss in the minced garlic and ginger. Stir constantly until fragrant, about 30 seconds; the kitchen will fill with a pungent aroma.
Add the julienned cabbage to the pan. Stir quickly, spreading it out to cook evenly. Sear for 3-4 minutes until edges turn golden-brown and cabbage begins to caramelize, releasing a sweet aroma.
Meanwhile, whisk together soy sauce, sesame oil, rice vinegar, and sugar in the small bowl to create the stir-fry sauce.
Pour the sauce over the cabbage and stir vigorously to coat all the vegetables evenly. Cook for another minute until the sauce thickens slightly and glistens.
Return the cooked chicken to the pan, tossing everything together. Cook for an additional minute to reheat the chicken and meld flavors. You should see the cabbage with some crispy, caramelized edges.
Sprinkle toasted sesame seeds and chili flakes over the top for added flavor and texture. Give everything one last toss.
Remove from heat and serve immediately, ensuring each plate has a balance of tender cabbage, juicy chicken, and crispy caramelized bits for a satisfying bite.