I actually know exactly what you are talking about. I lived in Saudi Arabia for 15 years and moved back home to California about 4 years ago. There are actually several forms of this pastry. The dough has a slightly rubbery consistency, but is very light and is made in several layers. It is called Al-Moutubeg. It is usually done with the saudi version of leeks and lamb or with the banana. I haven't been able to find anyone that makes it here, but I have found a recipe.
* 6 cups flour
* 2 eggs beaten with 1/2 cup corn oil
* 2 bundles leeks (medium sized)
* 1 teaspoon ground black pepper
* 1 1/2 lbs ground lamb or beef
* 3 eggs (beaten)
* 3 onions (finely chopped)
Sift flour, add the water and salt a little at a time, mixing dough until it becomes soft but pliable. Divide the dough into ten pieces, knead each piece well. Place on a tray sprinkled with a little water and let rise for at least one hour. Put ground beef in a saucepan with chopped onion, black pepper and salt. Stir over medium heat until cooked. Set aside until cool. Chop leeks and wash several times through a strainer; drain and put on a paper towel until excess water is absorbed. Add to ground beef.Take a piece of dough and cover in flour, roll out, place over back of hands and stretch until dough becomes quite thin. Place dough on worktop and trim uneven edges. Brush two tablespoons of egg and oil mixture over dough surface. Fold to form smaller squares. Place in frying pan or griddle over medium heat with one tablespoon of oil. Place pastry squares in pan and fry on both sides until golden brown. Repeat above method using five of the remaining pieces. With piece number six repeat as above to the folding stage. Place one fried pastry square in the center of the unfolded piece, cover generously with ground beef and three tablespoons of beaten egg. Fold into a square. Remember to sprinkle oil and egg mixture between layers. Fry in 3 tablespoons of oil over medium heat until both sides are golden brown. Repeat using remaining four pieces of dough. Serve hot. Serves 10-12.
There are several Saudi dishes that I wish I could find here in the US. At the moment I am looking for a green called Moulehiya, which is cooked into a stew and served over rice that I absolutely loved to have while I was there! My goal is to find an arab market that sells it frozen and chopped, so if anyone knows of it let me know!!