Bring the chicken broth to a boil over medium heat. Stir in the soy sauce, rice wine, sesame oil, and pepper, to taste. Turn up the heat slightly and add the cornstarch dissolved in the water, stirring quickly to thicken.
Move the saucepan to another burner and keep warm on low heat while preparing the egg foo yung omelet.
In a medium bowl, lightly beat the eggs with pepper, rice wine, and salt. Reserve.
Heat 1 tablespoon of the oil in a wok or frying pan over medium heat. When the oil is hot, add the onion and sausage. Stir-fry for 2 minutes, then remove from the pan with a slotted spoon and reserve.
Add 1 more tablespoon of the oil and stir-fry the sliced mushrooms until they’re browned. Remove from the pan and reserve.
Add the cooked sausages, onion, and mushrooms into the egg mixture along with the mung bean sprouts and napa cabbage.
Add the remaining tablespoon of oil to the pan. When the oil is hot, add the egg mixture. Cook until golden brown on the bottom.
Carefully turn over and cook the other side until golden brown.
Serve hot with the warmed sauce poured over the top and sprinkle with green onions, if using. Accompany with steamed rice. Enjoy.