To marinate the beef, in a bowl, whisk together the egg white, Shaoxing wine, salt, white pepper, and baking soda. Add the sliced beef and mix well until evenly coated. Let the beef marinate while preparing the remaining ingredients.
To prepare the sauce, in a bowl, mix together the soy sauce, dark soy sauce, oyster sauce, hoisin sauce, sugar, and water. In a small bowl, mix the cornstarch with the water to make a slurry. Set both aside.
To coat the beef, add the cornstarch to the marinated beef and mix until the slices are evenly coated.
To fry the beef, in a wok over high heat, heat the oil to about 350°F (177°C). Fry the beef in small batches for about 2 minutes until lightly crispy, then remove and drain.
To make the Mongolian beef, in a clean wok over high heat, add the cooking oil. Add the dried chilies and garlic and stir-fry for about 30 seconds until fragrant. Pour in the prepared sauce and bring it to a simmer, then stir in the slurry and cook until the sauce thickens. Return the beef to the wok and toss to coat evenly. Add the scallions, stir briefly, and serve hot.