For the marinade: Combine the marinade ingredients vinegar, lime juice, onion juice (see notes), yogurt, shawarma, and olive oil and massage the meat thoroughly. Cover with a plastic wrap and place in the fridge for 3 hours at least or preferably overnight. Before cooking the shawarma, let it drain any excess marinade’ liquids and let it come to room temperature.
For the Tahini sauce: Mix together the tahini, yogurt, lime juice and seasoning. Combine well and keep it in the fridge until you are ready to serve the shawarma.
For the shawarma: Melt “liyeh” (lamb fat) over medium-high heat in a large cast iron skillet or a normal skillet (that is not non-stick). Once the “liyeh” becomes fragrant and melts totally, add the shawarma in batches and in a single layer to the hot skillet. Don’t overcrowd the skillet. Cook them in batches. Each batch won't take more than 5-7 minutes to cook. Don’t overcook the beef shawarma to prevent it from toughening. Taste and adjust the seasoning. Add the diced tomatoes and diced red onions, to the cooked shawarma and stir for 2 minutes over medium heat. Turn off the heat and stir in the chopped parsley.
To smoke the shawarma: Place a piece of glowing charcoal in a heatproof dish or on a square of foil, and nestle it in the center of the cooked shawarma. Carefully pour a spoonful of hot oil over the charcoal to release smoke. Immediately cover the shawarma tightly with foil to trap the smoke, and let it infuse for 15–20 minutes in a turned-off oven.
To assemble: Use Lebanese bread, Palestinian shark bread or Persian/Armenian lavash bread, or soft brioche buns as Egyptians would do. Spread the bread with the tahini sauce, some harissa if you seek some extra heat. Add some pickled cucumber or pickled turnips and then add the shawarma. For an extra crunch, press the Lebanese bread filled with shawarma in the panini machine.
For serving: Serve the shawarma sandwich with fries, extra tahini sauce and an assortment of pickles.