Pat the beef cubes very dry. In a bowl, toss them with the soy sauce, oyster sauce, fish sauce, sugar, cornstarch, half the minced garlic, and the 1 teaspoon black pepper. Let it marinate at room temperature for 20 to 30 minutes, or cover and refrigerate up to overnight.
Make the dip while the beef sits. Stir the lime juice with the salt and the half teaspoon of black pepper in a small bowl until the salt dissolves. Arrange the watercress, cherry tomatoes, and cucumber on a serving platter.
Heat a large heavy skillet or wok over high heat until it is genuinely smoking hot. Add 1 tablespoon of oil. Lay in half the beef in a single layer and leave it alone for about 1 minute so a hard sear forms, then toss for another 30 to 60 seconds. The cubes should be deeply browned outside and still pink inside. Move them to a plate.
Add the remaining oil and sear the second batch the same way. Crowding the pan steams the meat instead of searing it, so cook in two batches even if you are tempted to rush.
Return all the beef to the pan, add the onion wedges and remaining garlic, and shake the pan hard a few times (this tossing is where the name comes from) for about 1 minute, until the onion softens at the edges but keeps its crunch. Add the butter now if using and toss to glaze.
Pile the beef and onion over the greens. Serve right away with the lime and pepper dip, and steamed rice or a fried egg on the side.