In a medium bowl, whisk together chicken broth, oyster sauce, Shaoxing wine, soy sauce, sugar, and cornstarch until smooth. Heat a tablespoon of peanut oil in a skillet over medium heat. Sauté minced garlic until fragrant, about 30 seconds, then add the sauce mixture and stir until it thickens, around 2-3 minutes. Set aside.

In a large bowl, mix ground chicken with cornstarch and a pinch of salt. Heat another tablespoon of peanut oil in a skillet over medium-high heat. Add the chicken mixture and cook for about 5-7 minutes until fully cooked. Transfer to a plate to cool.

In a large mixing bowl, crack the eggs and whisk until well combined. Add the cooked chicken, bean sprouts, chopped white onion, green onions, and white pepper. Mix gently to combine all ingredients evenly.

Heat a tablespoon of peanut oil in a non-stick skillet over medium heat. Scoop ladlefuls of the egg mixture into the skillet, cooking for 2-3 minutes on each side until golden brown. Repeat with the remaining mixture, adding oil as necessary.

Arrange the omelets on plates and drizzle the savory sauce over each. Serve hot with extra sauce on the side.