Heat your wok or deep skillet over medium-high heat until shimmering, then add the neutral oil.
Add the sliced chicken breasts to the hot oil, stirring constantly. Cook for 3-4 minutes until the chicken is golden and cooked through, with no pink remaining.
Add the minced garlic to the chicken, stirring quickly for about 30 seconds. The garlic should become fragrant, fragrant, and slightly golden, filling the air with aroma.
Push the chicken and garlic to one side of the pan, then add the thinly sliced cabbage in batches if necessary. Stir-fry for 2-3 minutes until the cabbage just begins to wilt and turn translucent, with edges starting to caramelize slightly.
Pour the soy sauce evenly over the cabbage and chicken, tossing everything together vigorously. The mixture should turn a glossy, smoky hue, and the cabbage will crisp slightly at the edges.
Continue stir-frying for another 1-2 minutes until the cabbage is tender but still crisp, and the chicken is fully cooked. The dish should smell savory with a hint of caramelization and smoky aroma.
Remove the pan from heat and drizzle the toasted sesame oil over the stir-fry. Toss gently to coat everything evenly with the fragrant, nutty oil.
Let the stir-fry rest for a minute to allow flavors to meld, then serve immediately while hot, garnished with optional scallions or sesame seeds if desired.