Start by marinading the beef shawarma: whisk together the yogurt, lemon juice, garlic and spices in a medium bowl. Add in the thinly sliced beef and let sit for 30 minutes at room temperature or in the refrigerator for up to overnight.
To cook the shawarma, you can either grill it on high heat for 3-4 minutes per side or saute in a hot skillet until beef is cooked through, about 8-10 minutes. Note: You'll want to remove excess marinade before cooking.
While the beef is cooking, whisk together the tahini sauce ingredients in a small bowl: tahini through salt. Check for seasoning and add more salt or cayenne to taste; set aside.
To assemble, lay the pitas flat and spread a bit of tahini sauce on the middle. Top with beef shawarma and any optional toppings such as onion, pickles, etc. Roll tightly then slice in half to serve.