Prepare the Shrimp: If your shrimp aren't already peeled and deveined, do that first. Then, give them a rough chop.
Whisk the Eggs: In a large bowl, whisk the eggs together with 1 tablespoon of soy sauce, 1 tablespoon of cornstarch, and a pinch of white pepper.
Combine Filling Ingredients: Add the chopped shrimp, bean sprouts, chopped onion, and sliced green onions to the egg mixture.
Heat the Oil: In a large skillet or wok, heat about 1/4 inch of vegetable oil over medium-high heat.
Cook the Patties: Once the oil is hot, carefully ladle about 1/2 cup of the egg mixture into the pan for each patty.
Fry Until Golden Brown: Cook the patties for about 3-4 minutes per side, or until they are golden brown and cooked through.
Drain Excess Oil: Once cooked, remove the patties from the skillet and place them on a plate lined with paper towels to drain any excess oil.
Make the Gravy: In a separate saucepan, combine the chicken broth, oyster sauce, 2 tablespoons of soy sauce, and sesame oil. Bring to a simmer.
Thicken the Gravy: Whisk together 2 tablespoons of cornstarch with 2 tablespoons of cold water. Slowly pour into gravy, whisking until thickened.
Serve: Pour the gravy over the Shrimp Egg Foo Young patties and serve immediately with steamed rice.