Heat 1 teaspoon of oil in a large skillet over medium heat. Add the eggs and season to taste with salt and pepper. Cook, undisturbed, until a flat omelet forms, about 3-4 minutes. Carefully flip the eggs and cook on the other side until done, 1-2 minutes more.
Remove the eggs from the pan and cut into strips. Cover to keep warm.
Wipe out the pan with a paper towel.
Heat the remaining 2 teaspoons of oil in the pan.
Add the chicken and cook, stirring occasionally, until meat is browned and cooked through, 4-5 minutes. Remove the chicken from the pan and place on a plate; cover to keep warm.
Add the cabbage, ginger and mushrooms to the pan and cook for 2-3 minutes or until mushrooms are tender and cabbage is wilted.
Return the chicken and eggs to the pan.
In a small bowl whisk together the soy sauce, hoisin sauce, sesame oil, honey and 1 tablespoon of water. Whisk in the cornstarch until smooth.
Add the sauce to the pan and turn the heat to high; bring to a boil. Boil for 30 seconds or just until sauce starts to thicken.
Serve immediately with tortillas, extra hoisin sauce and green onions.