Combine 1 tablespoon cornstarch with 2 tablespoons cold water in a small bowl. Whisk until completely smooth with no lumps visible.

Pour chicken broth into a medium saucepan over medium heat. Add soy sauce, oyster sauce, and sugar, then whisk to combine. Bring to a gentle simmer.

Give the cornstarch slurry a quick stir, then pour it into the simmering broth while whisking constantly. Continue whisking for 60 to 90 seconds until the gravy coats the back of a spoon. Reduce heat to low and cover.

Roughly chop the bean sprouts into 1 inch pieces. Slice the green onions thinly.

Crack all 6 eggs into a large mixing bowl. Beat vigorously with a whisk for 30 to 45 seconds until the whites and yolks are completely combined and uniform yellow.

Add bean sprouts, sliced green onions, diced protein if using, soy sauce, sesame oil, and white pepper to the beaten eggs. Fold gently with a spatula until evenly distributed.

Set your oven to 200 degrees Fahrenheit and place a sheet pan with a wire rack inside. Heat 1 and 1/2 tablespoons vegetable oil in a large skillet over medium high heat until shimmering.

Stir the egg mixture, then ladle about 1/4 cup portions into the hot skillet, leaving 2 inches between patties. Cook 3 to 4 patties per batch for 60 to 90 seconds until edges are golden and set.

Slide a thin spatula under each patty and flip in one confident motion. Cook the second side for 60 to 75 seconds until golden brown.

Transfer finished patties to the wire rack in the warm oven. Add remaining oil to the skillet and repeat the frying process with remaining egg mixture.

Return the gravy to medium heat and whisk until hot and smooth. If too thick, whisk in 1 to 2 tablespoons of hot water.

Arrange 2 patties per plate and ladle warm gravy generously over the top. Garnish with additional sliced green onions and sesame seeds if desired. Serve immediately.