Pat dry the flank steak on both sides and cut it into 1/4-inch strips, each measuring 3 inches long (lengthwise), against the grain. Sprinkle with the kosher salt and set it aside.
Make the shawarma seasoning: In a medium bowl, mix the cumin, coriander, paprika, garlic powder, black pepper, turmeric, cloves, cinnamon, nutmeg, and cardamon until thoroughly combined.
Make the marinade: In a large bowl, whisk together the olive oil, white vinegar, lemon juice, garlic, and shawarma seasoning until incorporated.
Add the flank steak strips and onions to the bowl and toss to fully coat.
Cover and refrigerate for at least 4 hours or overnight.
Make the lemon tahini sauce: In a bowl, whisk together the tahini paste, lemon juice, garlic, and kosher salt until blended. Slowly add the water while whisking until you reach your desired consistency. Adjust seasoning to taste. Set aside until ready to serve.
Cook the meat: Remove the flank steak from the refrigerator 30 minutes before cooking. Heat a large skillet (a cast iron skillet works best) on medium-high. Remove the flank steak and onions from the bowl and place on the skillet. Reduce heat to medium and stir occasionally as it browns. Cook for 4-6 minutes or until you achieve your desired doneness. Do not overcrowd the skillet. You may have to cook in 2-3 batches. Once cooked, place it on a plate or platter, loosely tent it with foil, and let it rest for 10 minutes before serving.
To serve as a wrap: Spread the tahini sauce on the bread (or inside of a pita pocket) and layer it with sliced tomatoes, pickles, cucumbers, lettuce and beef shawarma. Drizzle with more tahini sauce and if preferred with a squeeze of lemon juice right before serving.