In a bowl, combine chicken, ginger, garlic, and soy sauce. Let sit for 15–30 minutes.
Cook the chicken
Heat a large pan over medium-high heat. Cook the chicken until browned and cooked through. Remove and set aside.
Cook the vegetables (choose one option)
Option 1: Heat oil. Add mushrooms (if using) and cook until lightly browned. Add scallions and garlic. Stir in cabbage and carrots and cook until slightly softened.
Option 2: Heat oil. Add mushrooms (if using) and cook until lightly browned. Add onion and garlic. Add cabbage and carrots and cook until slightly softened.
Combine and serve
Return chicken to the pan and toss to combine. Season with salt and black pepper.
Drizzle with sesame oil and sprinkle red pepper flakes, if using.