Combine all the gravy ingredients in a small bowl and whisk until the cornstarch is fully dissolved. Set aside.
Crack the eggs into a large bowl and beat vigorously for about 60 seconds until frothy and no streaks of egg white remain. Stir in the jumbo shrimp, bean sprouts, shallots, toasted sesame oil, salt, and black pepper.
Heat vegetable oil in a wok or small 7-inch pan over medium-high heat. Pour in the egg mixture and evenly spread the jumbo shrimp, bean sprouts, and shallots across the pan with chopsticks, being careful not to break the base of the omelet. Cook the omelet completely untouched 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 and the shrimp are pink and opaque throughout, about 2 minutes. Transfer to a serving plate.
Reduce the heat to medium. Mix the gravy again, then pour it into the pan and simmer for 1 minute until thickened and glossy.
Pour the gravy over the omelet and garnish with chopped green onions. Serve immediately.