To cook the pork, in a wok or pan over high heat, add the cooking oil, then add the ground pork, salt, and white pepper. Stir-fry for about 3 minutes until the pork is fully cooked. Transfer to a plate and allow it to cool slightly.
To prepare the egg mixture, in a small bowl, mix the cornstarch with the water to make a slurry. In a separate bowl, whisk the eggs with the salt, then stir in the slurry. Add the cabbage, carrot, bean sprouts, scallions, and the cooked pork, then mix well.
To cook the egg foo young, in a wok or pan over medium heat, add about 1 tablespoon of cooking oil. Ladle some of the egg mixture into the pan and cook for about 2 minutes until the bottom is golden brown. Flip and cook the other side for another 2 minutes until fully set. Remove and repeat with the remaining mixture.
To make the gravy-style brown sauce, in a small bowl, mix the tapioca starch with the water to make a slurry. In a pot over medium heat, combine the chicken stock, soy sauce, oyster sauce, and sesame oil and bring to a gentle simmer. Stir in the slurry and cook until the sauce thickens and becomes glossy.
To serve, place the egg foo young patties on a plate and spoon the gravy-style brown sauce over the top.