Burek was an instance in my life of traveling where I was really excited to try a particular food once I got to the country I was going to, which in this case was Croatia. I arrived there in 2004, tried the Burek (in Split) and liked it. I found it to be really heavy and greasy, but that was part of the charm and I ate a great deal of them. Upon successive trips to Croatia, I always hunt these guys down for a quick meal in the morning, since later in the day, they get a bit soggy with the grease if they sit for awhile.
Now having been to Sarajevo and Belgrade, I can safely say that I have had the real Burek. The one in Croatia is an impostor and presenting itself under false pretenses. They are really what the Serbs call a ‘gibanica’. In reality, in Sarajevo, the Burek is just a meat pastry, served in this rolled-up filo dough around the meat filling. It has been cooked under a sač, which is basically a pile of coals that sit on a tray above a large, round pan, where the Burek has been coiled up. Once cooked, you often will buy them by weight and they are a chunk of heaven.
In case you are rolling your eyes and thinking, “Yeah, great. More Balkan meat…”, I need to assure you that there are more kinds than just the meat, but those are the real Burek. For reference there are:

Sirnica w/ cheese
Zeljanica w/ spinach and cheese
Tikvenjača w/ pumpkin
Krompiruša w/ potatoes
Jabukovača w/ apples and sweet
Višnjevača w/ sour cherries and sweet

While all collectively called ‘pita’ (yes, confusing to those in America, since pita is something different for us), I haven’t tried all of these, but the Sirnica and the Zeljanica are both quite good as well. Admittedly, I keep coming back to the meat one. It must be the Croat in me, although ironically, the Croatian ones simply aren’t as good and they also just call them all Burek with some kind of a ‘s’ and then the filling at the end like ‘s krompirom’ which means, ‘with potatoes’. Cheeky, yes. When in Bosnia Herzegovina or Serbia, hit the Burek and hit it hard.
Burek is Also... The Bomb