Non-cow's milk replacement for Parmesan cheese in Genovese pesto
Finding a non-cow subsitute for parmesan is a difficult task - Grana, the closest, is made from cow milk as well so it's no good.
You can try using Pecorino which is made from sheep milk, and has a slightly stronger flavour.
I've never tried it personally, but it's not rare in some regions of Italy to make pesto with pecorino, so it's definitely worth a try!