Whisk Gravy: Combine oyster sauce, cornstarch, regular soy sauce, Shaoxing wine, toasted sesame oil, and low-sodium chicken broth in a small bowl. Set the mixture aside.
Crack eggs into a large bowl and beat until smooth and frothy. Stir in jumbo shrimp, bean sprouts, shallots, toasted sesame oil, salt, and black pepper.
Heat vegetable oil in a small pan or a wok over medium-high heat. Pour in the egg mixture and evenly spread the jumbo shrimp, bean sprouts, and shallots with chopsticks, being careful not to break up the base of the omelet.
Cook until the bottom is golden brown and crispy, about 3 minutes. Carefully flip with a large spatula, or slide the omelet onto a large plate and invert it back into the pan. Cook the other side until golden brown, about 2 minutes. Transfer to a serving plate.
Reduce the heat to medium. Pour the prepared gravy into the pan and simmer for 1 minute until thickened.
Pour the gravy over the omelet and garnish with chopped green onions.