Pitas,flatbread, or naan (I used naan from my freezer...)
Yogurt sauce (above)
Feta crumbles, optional
Combine all sauce ingredients, then refrigerate prepared sauce so that the flavors can meld while you cook the rest of the recipe.
Combine ground beef and seasonings in a large bowl, then form into several patties. Fry these in a 12.5" cast iron skillet over medium heat until cooked through (about 7 minutes a side).
Remove to a cutting board and let cool for about 10 minutes, then slice.
Serve the sliced ground beef gyro meat in pitas, on naan, or on flatbread, topped with tomato, lettuce, onions, yogurt sauce, and (optional) feta.
The consistency here will not be the same as you get with real gyros, but the flavor is pretty close (as close as you're going to get without adding the lamb!). If you're low carb or gluten free, just enjoy your gyro in lettuce or on an appropriate wrap.