Just found this thread.
If you’re open to “that weird Japanese cartoon stuff”, check out Amon Saga. It really is weird though, even by the standards of anime, and all the more so for being vintage (1980s). Still, it’s obviously inspired in part by the Conan films, even if it’s more high-fantasy. It also has a bit of a B-movie feel, but given the subject of this thread, that should hardly be a disqualifier in and of itself.
If nothing else, you can skip-forward through it on Youtube (in fact I recommend skip-forwarding to be spared most of the abominable English dub!).
I’m sure that if one were to comb through the whole corpus of anime movies, TV shows and OVAs, one would end up with a small heap of “desert fantasy” type stories, but much of it is obscure, and the Japanese twist on Western fantasy definitely isn’t for everyone.