Heat olive oil in a 12-inch skillet over medium-high heat.
Add shredded chicken in a single layer and let sit for 5 minutes.
Toss chicken gently to crisp up all sides.
Remove from heat and stir in ginger, lemongrass, and garlic.
Let chicken cool slightly while you prepare salad base.
In a large bowl, combine shredded cabbage, herbs, red onion, lime juice, zest, and apple.
Add cooled chicken and toss to combine.
Drizzle extra olive oil if needed and season with kosher salt to taste.
Serve immediately or store for later.