In a large skillet or wok, heat 2 tablespoons oil over medium-high heat. Once hot, add chicken and cook until browned and cooked through, about 6-7 minutes. Remove chicken to a plate and reserve.
Add remaining oil and add shitake mushrooms. Cook until browned, about 8 minutes. Once browned, add scallions, carrot, garlic, pepper and cabbage, and sauté until all veggies are soft and slightly browned, about 6-7 minutes.