I made this up as I went along, and I didn't write down any amounts because I was sure I'd remember it. Right. So take the amounts listed below as a guide of where to start, and adjust according to your taste and/or what you've got in your pantry.
Take 1 pound of ground beef and break it up into little pieces with your fingers. Add about 2 ounces of crumbled feta cheese, a couple good shakes of zatar, a couple tablespoons of minced fresh oregano, a couple tablespoons of minced green onion, some garlic powder, and some Penzey's Turkish seasoning. Mix it all together with your hands, making sure you distribute the good stuff evenly. Form into four patties.
Grill as you would normal burgers, and toast the burger buns at the same time. When the burgers are done, slather a thick layer of baba ghanouj on the top half of each burger bun before putting them on the patties. If you have any pickled turnips you can throw some slices on there, too, but the burgers are also great without them.