Place the beef in a bowl and add the onion, garlic, lemon juice, vinegar and olive oil. Add in the cumin, turmeric, coriander, cinnamon, allspice, paprika, cardamom, salt and pepper. Using your hands or a pair of tongs, mix the beef with the spices and olive oil mixture and make sure all pieces are well coated. Cover the bowl with a plastic wrap and marinate for 1 to 2 hours.
Heat a large cast iron skillet or a nonstick pan over medium high heat. Once the pan is hot, transfer the beef to the pan and sear until fully cooked, about 8 to 12 minutes. If your pan is not large enough, cook the beef in batches.
To make the tahini sauce, mix the tahini with lemon juice, garlic, salt and pepper. If you like the sauce runnier, add a little bit of water.
Once the beef shawarma is ready, start assembling the sandwich. Start by placing the beef shawarma on the pita, top with tahini sauce, turnip pickles, cucumber pickles, sumac onion, fries, lettuce and tomatoes. Wrap tightly and cut in half if preferred.