This is a little weird; my Greek family is from Jerusalem and mostly makes Levantine dishes with a Greek twist. Gyros were invented after WWII in mainland Greece, so they’re not in my repertoire.
They also are made on a big rotisserie oven, so it’s not trivial to replicate. But I found this recipe from Alton Brown, where you make them in the oven, so I figured it was worth a try.
They came out good. I think if I were to do them again I’d fry the thin slices in the oil that comes off; that’s supposed to make them crisper. But even soft they were spicy delicious.