In a medium bowl, whisk together 1 tablespoon each soy sauce, oyster sauce and rice wine. Add the sugar and continue to whisk until completely dissolved. Stir in the tapioca starch and continue stirring until smooth. Add the sesame oil and beef, and mix well. Marinate for 20 minutes. Drain and discard the excess marinade.
Bring a large pot of water to a boil. Cook the noodles until 1 minute shy of done and drain. (We'll finish cooking the noodles at the end).
Heat 1 tablespoon of the vegetable oil in a skillet or wok over high heat and stir-fry the garlic until fragrant, about 1o seconds. Add the beef and stir-fry until tender, 1 to 2 minutes. Transfer to a plate. Add the remaining tablespoon of oil and when hot, add the Chinese broccoli, stir frying so that the oil coats the Chinese broccoli. Pour in the 1/4 cup of the stock, turn the heat to medium-low and cover with a tight fitting lid. Cook the Chinese broccoli until tender, 3 to 5 minutes. Transfer the Chinese broccoli to the same plate.
Add the remaining cup of stock and the remaining 2 tablespoons each of soy sauce, oyster sauce, and rice wine to the same skillet and bring to a boil over high heat.
Add the noodles and cook until the liquid has almost completely evaporated, leaving the noodles lightly moistened,2 to 3 minutes. Return the beef and broccoli to the skillet and toss to mix the ingredients thoroughly. Season with pepper to taste and serve.