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Heat 1 tbsp 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.
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Remove the egg from the pan and cut into strips. Cover to keep warm.
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Wipe out the pan with a paper towel.
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Heat 2 tbsp oil in the pan. Add the chicken and cook, stirring occasionally, until meat is browned and cooked through, 4 to 5 minutes. Remove the chicken from the pan and place on a plate; cover to keep warm.
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Add the cabbage, ginger and mushrooms to the pan and cook for 2-3 minutes or until the mushrooms are tender and the cabbage is wilted.
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Return the chicken and eggs to the pan.
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In a small bowl, whisk together the soy sauce, hoisin sauce, sesame oil, honey and 1 tbsp of water. Whisk in the cornstarch until smooth.
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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.
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Serve immediately with tortillas, extra hoisin sauce and green onions.