01 - Whisk together eggs, milk, salt, and white pepper in a large bowl until smooth and fully incorporated.
02 - Add bean sprouts, carrots, green onions, mushrooms, bell pepper, and diced protein to the egg mixture. Stir until evenly distributed.
03 - Heat 2 to 3 tablespoons vegetable oil in a large nonstick skillet or wok over medium-high heat until shimmering.
04 - Scoop approximately 1/2 cup of mixture per patty into the hot pan. Gently flatten and cook 2 to 3 patties at a time, adjusting for pan size.
05 - Fry each side for 2 to 3 minutes until golden brown and crispy. Carefully flip and cook opposite side. Transfer to paper towel-lined plate. Repeat with remaining mixture, adding oil as needed.
06 - Combine chicken broth, soy sauce, oyster sauce if using, sesame oil, and white pepper in a small saucepan. Bring to a simmer over medium heat.
07 - Whisk cornstarch with cold water in a small bowl to form a slurry. Stir into simmering sauce and cook for 1 to 2 minutes until thickened and glossy.
08 - Plate crispy patties hot and drizzle generously with savory gravy. Garnish with additional green onions if desired.