In a bowl, stir together the chicken, cornstarch, and soy
sauce.

Add about a tablespoon of the oil to a large nonstick skillet and heat over medium-high heat. When the pan is hot, add the onion and cook, stirring occasionally, for a minute or so. Add the chicken and break it
up with a spatula, spreading it out in the pan in a thin layer. Cook for a
minute or two until the bottom begins to brown, then stir and flip the chicken, breaking it up into smaller pieces. Cook for another minute or two until the chicken is cooked through. Add the shredded carrots and stir to mix. Remove the skillet from the heat and let cool.

While the chicken mixture cools, make the sauce. In a small saucepan, combine the broth or water, soy sauce, oyster sauce, wine, and cornstarch and cook over medium heat. Bring to a simmer and cook, stirring occasionally, for a few minutes, until the sauce thickens a bit. Remove from the heat.

In a medium bowl, lightly whisk the eggs with soy sauce, sesame oil, and white pepper. Add the scallions, bean sprouts, and the cooked (cooled) chicken mixture to the eggs and stir to mix.

Add 1 tablespoon of the oil to a nonstick skillet. Swirl the pan to distribute the oil evenly. When the pan is hot, add about 1/2 cup of the
egg mixture to the skillet to create a patty about 4 inches across. Repeat 2 or 3 more times, depending on the size of your skillet, to make additional patties. Add the mixture to the pan slowly and then immediately use a spatula to push the edges in so that the egg doesn’t run all over the pan. You want to keep each ladleful of egg together in a rough patty shape.

Cook the patties for about 2 minutes, until they are set on the bottom, and then flip them over to cook on the second side. Cook for 1 to 2 minutes more, until the second side is lightly browned. Remove the cooked patties from the skillet, and cook the remaining egg mixture in the same way.

Serve the patties over rice with the sauce drizzled over the top and garnished with sliced green onions.