Step 1If using sangak, cut it crosswise into 4 pieces and cut each of those in half lengthwise. You’ll have 8 roughly rectangular pieces about 10 inches by 6 inches. Heat the sangak or lavash in a single layer in a 350-degree oven or on a griddle until warmed through but still soft and pliable, 1 to 2 minutes, depending on thickness.
Step 2To make a wrap, place a piece of flatbread on a plate or work surface, browned side down (in “landscape” orientation if rectangular in shape). Smear generously with labne, leaving a 2-inch border along the bottom edge. Season the labne generously with za’atar, top with generous amount of chopped parsley, and drizzle with olive oil. Spoon some secret sauce over, add hot sauce as desired, and scatter tomatoes over.
Step 3Fold the bottom border up. Fold left side edge in halfway toward the middle of the flatbread. Repeat with the right side. Bring the two folded side edges together to meet, as though closing a book. Repeat with the remaining flatbread pieces and fillings.