Trim any excess fat from the steaks, cut into 1-inch cubes, and place in a large nonreactive bowl.
Place onion, garlic, lime juice, salt, pepper, and saffron or cumin, in a food processor and process until smooth. Pour mixture over meat, toss to coat, cover and marinate 30 minutes at room temperature, or up to 12 hours in the refrigerator.
When ready to cook, heat grill to medium heat (350 degrees F) and oil well. Thread meat on skewers, leaving at least 1/2-inch space between each piece of meat. In a small bowl and the tomatoes, drizzle with oil, season with salt and pepper, and toss to coat thoroughly. Place meat and tomatoes on grill. Cook meat, turning once, until charred and medium-rare, about 7 to 10 minutes. Cook tomatoes, turning rarely, until blistered and soft, about 10 minutes.
Remove meat from skewers and have guests assemble their own sandwiches with meat, tomatoes, lavash, yogurt, and cilantro.