Making or buying a lavash bread that's flexible enough to make the traditional U-shape is tricky, so feel free to fold it more like you would a burrito. You can even substitute with store bought flour tortillas to save time.
Make the sumac onions. Into a medium mixing bowl, add the onion, sumac, and a small pinch of salt. Use your hands to massage the seasoning into the onions, softening them and working in the flavor.
Add more to the onions. Into the bowl with the onions, add the tomatoes, parsley, 1/2 teaspoon of the Aleppo pepper (if using), and more salt to taste. Juice in one lemon. Toss the ingredients together to combine, then slice the remaining lemon into wedges. Set the salad and lemon wedges aside while you cook the steak.
Sear the steak. Trim the steak of any fat and slice into small pieces, each about the size of a sugar cube. Add the olive oil to a medium pan over medium-high heat. When the oil is shimmering (but before it starts to smoke), add the steak pieces. Stir until they expel and reabsorb their water and become golden, about 8 minutes.
Finish the steak. Season the steak with the paprika, remaining 1/2 teaspoon Aleppo pepper (if using), and a large pinch of salt (about 1 teaspoon). Stir to coat, then add the water. Turn the heat to medium and allow the mixture to simmer for 5 minutes or so to slightly reduce.
Soak the lavash. Turn the heat to low, keep the meat in the pan, and cover it with a piece of lavash. Carefully press with your hands or a spatula to encourage the bread to soak up the juice and soften from the steam. Be patient here—give the bread at least 30 seconds to soak in the flavor. The bread should be a nice golden hue.
Build the wrap. Use tongs to transfer the lavash to your serving plate with the soaked side facing up. Spoon the meat in one thin line near the edge of the bread and spoon a little gravy from the pan over top. Add a line of the tomato and onion salad. Be careful not to overfill it.
Roll and enjoy. Roll the lavash over the steak and salad, pulling towards you and rolling from top to bottom to make a long, extra skinny burrito or tube. Gently bend into a U-shape. Enjoy from both sides, squeezing fresh lemon juice into the top opening as you go. Your final bite will be the base of the U where all the delicious juices have pooled. Note: Depending on your lavash bread, the U-shape can be tricky! If your lavash starts to break, simply enjoy it more like a standard wrap or wrap it like a burrito.
Repeat. Repeat the filing and rolling with the remaining lavash bread, enjoying the tantuni while it’s hot and fresh.
Notes
Store bought lavash tends to be brittle and dry. I've found tortillas to be the best substitute for this recipe. That said, if you'd like to use a store-bought lavash, look for the softer versions that are on the thicker side. Sprinkle them with water and gently heat to soften.
Give the bread plenty of time to soak in the gravy. This is what makes tantuni so special! Press down and be patient as it soaks in the flavor.