In the bottom of large mixing bowl, add the shawarma spices. Add the olive oil, vinegar, and zest and juice of one lemon. Using a spoon, mix to combine.
Using a chef’s knife, cut the flap steak against the grain into thin bite-size slices (no more than ¼-inch in thickness).
Add the sliced meat to the bowl. Season with kosher salt and black pepper. Add the garlic and onions. Using a pair of tongs, toss very well to make sure the meat is well-coated with the marinade. Set aside to marinate at room temperature for a few minutes (or, if you have the time, cover and refrigerate for a couple of hours).
Heat a large cast iron grill pan or skillet over high heat. Using a pair of tongs, add the meat pieces, spreading them as much as you are able. Cook over high heat for anywhere between 8 and 15 minutes, until the meat is fully cooked. (If you like less liquid in your pan and extra char on the meat, you'll likely cook it for about 15 minutes. And if your pan is not large enough, cook the meat in batches).
While the meat is cooking, prepare the pita pockets and fixings. Make my 3-ingredient Mediterranean salad with tomatoes, cucumbers, and parsley. Make the tahini sauce. And prepare your pickled cucumbers, if using.
Assemble the shawarma sandwiches. Open up your pita pockets and load them up with the beef shawarma, salad, and finish with a generous drizzle of tahini sauce. Serve immediately!
This recipe makes 8 pita pocket sandwiches. The serving size is 1 pita pocket sandwich.