Slice the chicken thighs into thin strips, about ¼ of an inch thick and add to a large mixing bowl.
In a food processor or blender add the garlic, hot pepper paste, yogurt, vinegar or lemon juice, olive oil, and shawarma spice blend. Blend until nice and smooth then pour over the chicken and mix to coat all the chicken in the marinade. Let sit for at least 30 minutes and up to 24 hours.
Preheat your broiler on high and add a heavy-duty sheet tray to preheat. Remove the sheet tray once hot and add the tallow or ghee to melt. Carefully spread the marinated chicken out into one even layer. Broil for 8-10 minutes until the chicken begins to brown and char slightly, flip the chicken to cook the other side and return to the broiler for another 8-10 minutes, or until all the chicken is nicely charred.
Remove the pan from the broiler and transfer the chicken to a large shallow pan or heatproof dish. Reserve the sheet tray to dip the pita into.
Fill a small bowl with oil and set it in the center of the cooked chicken. Drop in a hot coal to create smoke then over the pot or dish and allow the chicken to smoke for 4-5 minutes. Discard the oil and coal and set the chicken aside.
Dip your pita into any remaining pan drippings from the chicken tray then smear the middle with a heaping tablespoon of toum. Add a portion of cooked chicken on top of the toum, then a layer of spicy pickles. Roll up tightly and brush with hot pepper paste mixed with a little water on each side.
Toast the wrap, seam side down, in a clean pan on medium-low, serve with extra toum and pomegranate molasses for drizzling over each bite.