Make the gravy base: In a small saucepan, whisk together chicken broth, soy sauce, oyster sauce, sugar, and white pepper. Bring to a gentle simmer over medium heat.
Thicken the gravy: Stir the cornstarch slurry to recombine, then slowly whisk it into the simmering broth.
Cook 1–2 minutes until glossy and thick enough to coat a spoon. Stir in sesame oil, turn off heat, and keep warm.
Prep the egg mixture: In a large bowl, beat the eggs until well combined but not frothy. Add chicken, bean sprouts, cabbage, green onions, onion, mushrooms, carrot, and garlic.
Season with soy sauce, sesame oil, white pepper, and salt. Stir gently until evenly mixed.
Heat the pan: Set a large nonstick skillet or well-seasoned wok over medium-high heat. Add 1 tablespoon oil and swirl to coat.
The pan is ready when a drop of egg sizzles on contact.
Portion and fry: Scoop about 1/2 cup of the egg mixture into the hot pan, forming a small round patty about 4–5 inches wide. Fry 2–3 minutes until the edges are golden and set.
Flip and finish: Carefully flip using a wide spatula. Cook another 2–3 minutes until cooked through and nicely browned.
Transfer to a plate and keep warm. Repeat with remaining mixture, adding more oil as needed.
Serve: Spoon warm gravy over each egg foo young patty. Garnish with sliced green onions or cilantro.
Serve with hot rice.