Cut the beef into 1-inch cubes.
In a bowl, combine the beef with 3 cloves minced garlic, soy sauce, oyster sauce, fish sauce, sugar, black pepper, and sesame oil. Marinate for at least 15 minutes.
Prepare the dipping sauce: In a small bowl, combine lime juice, salt, and the remaining black pepper.
Arrange the lettuce and sliced tomatoes on a serving platter.
Heat vegetable oil in a large wok or skillet over high heat until smoking.
Add the beef in a single layer and sear for 1-2 minutes per side until nicely browned. Do this in batches if necessary to avoid overcrowding. Remove beef and set aside.
Melt butter in the same wok. Add the remaining minced garlic and yellow onion wedges. Sauté until the onions are slightly softened, about 2-3 minutes.
Return the beef to the wok. Stir-fry vigorously for 1-2 minutes until the beef is cooked to your desired doneness. This rapid stir-frying motion gives the dish its "Shaking Beef" name.
Stir in the chopped green onions.
Transfer the beef and onions to the serving platter with the lettuce and tomatoes. Serve immediately with the lime dipping sauce.
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