Crack the eggs into a large bowl and beat with a fork. Add the bean sprouts, ground pork, shrimp, scallions, sesame oil, Shaoxing wine (if using), oyster sauce, soy sauce, sugar, and white pepper. Stir well until everything is evenly combined and the oyster sauce is fully dissolved.
Heat a wok or skillet over high heat and add the oil. Once the oil is hot, ladle about one-third of the egg mixture into the pan, forming an omelet about 4 to 5 inches (10 to 12 cm) wide.
As the omelet begins to set, use a pair of chopsticks to gently gather the bean sprouts, pork, shrimp, and scallions toward the center, making the middle slightly thicker. Cook for about 3 minutes, or until the bottom is golden brown and set.
Carefully flip the omelet and cook for another 2 to 3 minutes, or until the other side is golden brown, puffed up, and the pork and shrimp are fully cooked. Repeat with the remaining egg mixture to make a total of 3 omelets. Serve immediately with steamed rice.