Make the gravy: In a small saucepan, heat oil over medium-low. Add garlic and cook, stirring, until fragrant, 1 minute. Reserve 2 tablespoons of the broth in a small bowl; add the remaining broth to the pan. Add oyster sauce and soy sauce and bring to a boil. Simmer briskly, stirring occasionally, until the flavors have melded and the sauce reduced to about 1 cup, about 10 minutes.
Add cornstarch to the reserved broth and whisk until smooth, then add to the sauce. Cook, stirring, until thickened to a gravy consistency, about 1 minute longer. Stir in sesame oil and season with salt and pepper. Keep warm.
Make the omelets: In a large (12-inch) cast-iron or nonstick skillet, heat 1/3 inch of oil over medium-high until an instant-read thermometer registers 325 to 350 degrees, 4 to 6 minutes. (The oil should be shimmering and a drop of the egg mixture in the oil should sizzle immediately.) When the oil is almost ready, combine eggs, shrimp, mung bean sprouts and scallions in a large bowl and season with salt and pepper. Using a fork, break the egg yolks and fold the mixture just until well incorporated. (Don’t overbeat or the eggs will spread too much during frying.)
Using half of the batter, add 2 ladlefuls of the egg mixture to the oil to form 2 omelets. (They will bubble immediately.) Cook, basting the top with the hot oil, until golden underneath and just set, about 2 minutes. Flip, using tongs or a spatula and fork, and cook, basting with the oil, until golden on the second side and cooked through, about 1 minute longer. Transfer to a paper towel-lined plate to drain and season with salt. Repeat with the remaining egg mixture to form 2 more omelets.
Arrange the omelets on plates and top with some of the gravy. Garnish with scallions and serve with the remaining sauce on the side.
Source:
cooking.nytimes.com