Heat 1 tablespoon vegetable oil in a large skillet over high heat.
Add the eggs and scramble. Transfer to a plate.
Heat remaining 1 tablespoon vegetable oil in the skillet.
Add the ginger and garlic to the skillet, and cook 1 minute.
Add the cabbage and mushrooms, and cook until cabbage is wilted, about 5 minutes.
Stir in the soy sauce, hoisin sauce, and sesame oil.
Add the chicken and scrambled eggs to the skillet, and cook until the chicken is heated through, about 2 minutes.
Serve over rice or in warm tortillas, and garnish with scallions and extra hoison if desired.