You can check in Wikipedia the meaning of the word burek, but basically it is an unbelievably tasty home made phyllo dough pastry, that was originally developed in Turkey.
Although you can always bake burek with phyllo dough from the store ( you can find it in the freezer section even in Walmart, Athens Food are the most popular here in US), the taste is not the same.
The recipe can seem a little intimidating, but trust me, it is easier than it sounds, I have a lot of pictures step by step( thanks to Alex!) you can follow, but believe me the taste of this thing is worth every single minute you spend making it!

The preparation time is 1 hour and 30 minutes, as you are waiting 30 minutes for the dough to rest, so you can say it is approximately one hour. If you have a pasta machine, you can cut the preparation time more than a half, but I don’t so I use a rolling pin instead.

The baking time is around 40 min.

Ingredients:

For the phyllo dough-
8 cups sifted flour
8 tsp ( 4 oz or 1 stick) melted butter
1 egg
1 tsp salt
2 cups hot water

For the filling-
8 tsp melted butter
2 cups feta cheese ( grated or mashed)

For the topping-
3 eggs
4 tbsp yogurt
1/8 tsp baking soda

Sift 7 cups of flour in a big baking pan. Make a whole in the middle and put the flour close to the ends of the pan so it looks a little bit like a volcano).

In the middle pour the hot water, add the egg, the salt and the melted butter. With a tablespoon start stirring and gradually add a little bit of flour from the sides. When the mixture gets ticker, start kneading the dough with hands as you sprinkle flour from the side of the pan over the dough. Before you knead it really well it has to look like this:

Continue to knead until you it has nice and smoot surface and you use all of the flour in the baking pan.
Place a big piece of aluminum foil on a big table so you can have room to roll out the dough.
*Tip- use a scotch tape to attach it to the table, so it does not move when you are rolling the dough out.

Sprinkle some flour over the aluminum foil and divide the dough into 5 “balls” (see the picture)
Sprinkle some flour on top of them so they don’t get dry and leave them to rest for 30 minutes.

While the dough is resting, in a bowl mix together the ingredients for the topping- 3 eggs, 4 tbsp yogurt and 1/8 tsp baking soda. Stir thoroughly and set aside.

You will need to make 5 (almost) square sheets of dough. If you have ever rolled out a dough before, skip this section, but if not, follow this pattern:

1. sprinkle flour below the dough ball and start rolling it out.

2. sprinkle flour on top of the dough ( see the picture)

3. roll the dough out using both hands, slide and push at the same time.

4. sprinkle flour on top of the dough, then gently rub it on its surface with your hand.

5. roll the dough ON the rolling pin

6. Lift the roling pin and unroll the dough on the table upside down.

7. Sprinkle flour over the sheet of dough and repeat the whole process until you get really really thin sheet of dough ( as thin as a sheet of paper, almost transparent).

Don’t get discouraged if your sheet tears here and there, this wont affect the finished product that much, just try your best!

After the sheet is ready, brush with melted butter ( the remaining 8 tsp for the filling).

Then sprinkle with the feta cheese ( picture below)

and start to roll the dough from the long side inwards

Then place the phyllo dough roll in a round greased pan in a spiral from the outside in.( if you don’t have round pan that is bigger than 10 inch, you can use square one instead). When you roll out all of the dough, and place it in the pan, brush it on top with the butter you have left.
Preheat the oven at 350 F.

Then spread the topping evenly over the burek.

Place the pan in the oven and bake for 45 min on 350F or until golden brown on top ( see the picture).Leave it to cool down for at least 15 minutes, then cut.
Serve warm.
*I promise, for the people that think it is difficult to post in the next couple of days a recipe for phyllo Bulgarian banitsa, which is a lot easier to make, but still delicious.

P.S: Recipe in Bulgarian here