The traditional version of Bulgarian musaka is made from potatoes and minced meat (usually 70% veal and 30% pork). The zalivka (what you pour on top of it) is made from yogurt and eggs. I have never had Bulgarian musaka served where the zalivka included any sort of cheese - either sirene, kashkaval, or something else. Some people add a bit of flour in the yogurt and egg mixture to thicken it a bit. I'd have to say that compared to other versions, the traditional Bulgarian musaka is quite simple and healthy (don't get me wrong but while the bechamel sause may taste great, I'd say that yogurt and eggs is probably less calories and much healthier). 
The way I make musaka is I take the minced meat; add salt and some spices like chubritza, black pepper, and paprika. I put some oil in a pan and heat it, then add finely chopped onions until they become translucent. Then I add the minced meat. Once the meat no longer looks raw, I add the finely diced potatoes. I mix it all well, add some more salt and spices, then add some tomatoes from a jar and a bit of warm water. After that I pour everything in big "tava" (a large round baking tray that has higher walls than baking trays you are used to in the US) and put in the oven. I bake until the potatoes are fully cooked (but make sure there is still a little juice in the dish as you don't want it to be too dry). Meanwhile, I would have made the mixture of yogurt and eggs (I usually put more yogurt and maybe 2 eggs and whisk it all well together) and I will pour it on top of the potato and minced meat mixture. Then I will return it to the oven until the mixture looks cooked but is not dry. And then it's done and ready to eat. Often times it tastes better the next day - the flavors have a chance to mix overnight. The key to a really good musaka is quality ingredients (although this is true for pretty much everything); you want to have good fresh potatoes and fresh minced meat.