Some searching on the web revealed to me that börek comes in many varieties, both with meat and with cheese, but that the one I tasted in several restaurants isn't really the most common. It is very yummy however, so I wish to share it with you anyway.

Börek with feta and mint

You need:

Mash the feta and mix trough the pepper, nutmeg, and herbs of your choice. Mint is best in my opinion, as it makes an interesting contrast with the salty taste of the cheese. I suppose you could also use a mixture of herbs, experiment!.

Cut the filo pastry into strips with a width of about 7.5 cm (3''). Brush them on one side with a bit of butter or olive oil (make sure to keep the strips you're not yet using moist with oil, butter, or under a moist tea towel or something).
Put some filling (about a teaspoon full) on the non-brushed side near the end and roll up into a triangle as above, or into a cigar shape. Fold the long sides of the pastry to the inside if you use the cigar shape, to keep the filling from falling out.

Put your börek onto a greased baking tray, brush them with a bit of oil or butter again, and bake them for 25 minutes at 180 degrees C.

The börek can be served with tomato sauce if you like, or you can just eat them without. Enjoy.