In a bowl combine the onion, herbs and spices. Mix well and set aside.
Trim and remove all fat from the beef, cut into small dice. Transfer to a bowl and mix with oil and spices.
Heat a skillet over medium high heat and add butter to melt. Add seasoned beef and stir quickly to cook for several minutes until no longer pink. Add water and quickly toss with the meat. Lay a skillet sized piece of lavash or bread of choice (even a tortilla works) on top to steam. Cook until water has evaporated and you hear meat sizzle in skillet.
Remove bread and lay top side on work surface. Add a few tablespoons of the onion mixture in a row across lower area of bread, then a row of tomatoes and then some beef. Roll and wrap, cut in half and serve immediately. Repeat with others.
Notes
I have also substituted flank steak sliced thin and diced.