In a large wok or skillet, heat 2 tablespoons oil over medium high heat.
Once the wok is hot, add the sliced onions and preserved cabbage. Add the ground pork, breaking up the pieces. Stir in the sugar, salt, pepper, and 2 tablespoons of the mushroom soy sauce. Continue to break up the pork pieces and cook until browned, about 5 minutes. Remove the wok from heat and set aside.
In a large bowl, beat the eggs with the remaining 2 teaspoons mushroom soy sauce. Heat a 12 inch skillet over medium heat and lightly drizzle some of the remaining oil.
Once heated, add enough of the eggs to coat the bottom of the skillet. Tilt the skillet to even out the eggs across the bottom and up the sides.
Cover one side of the omelet with the pork mixture. Sprinkle with some of the thinly sliced green onions. Cook until the eggs are almost set, about 2 minutes.
Fold the omelet over the filling and cook until sealed, another 2 minutes. Garnish with cilantro, fresh vegetables, and serve immediately with Jasmine rice.