Season the chicken well with salt and pepper.
Heat a non-stick pan over medium-high heat; Once hot, add the oil and stir-fry the chicken until nicely browned. Then remove the chicken and set aside.
Lower the heat to medium. Add the pepper and onion to the pan and saute until soft. Then add the garlic, ginger, and cabbage mix. Saute until the garlic and ginger are fragrant.
Stir in the broth, soy sauce, oyster sauce, and half of the scallions. Add the chicken back to the pan and bring to a low simmer until it thickens to a syrup consistency. (if needed add cornstarch dissolved in water a little at a time to thicken). Season with salt and pepper to taste.
In the meatime, heat a nonstick pan over medium heat. Once hot, add a small amount of oil, eggs, and remaining scallions. Season with salt and pepper. Cook until the bottom sets, then flip over and cook until no longer runny but still moist (not overcooked). Remove from the heat.
Serve the chicken over the omelet. Garnish with scallions. Fortune cookie on the side.