My family loves Genovese pesto and we'd started making our own (with varied success). One of our number has been diagnosed as intolerant to cow's milk. This rules out pretty much all shop-bought varieties, so we now have to take the homemade route seriously. To help us out, please can you suggest non-cow's milk cheeses that we could use instead of Parmesan?
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!
I've been making my pesto with Pecorino Romano (may just be labeled 'Romano'; also, look for the brand name Locatelli) for years, even before I figure out I had issues with cow's milk. (note, there are a few different versions of Pecorino, as it basically means 'from sheep'; Pecorino Romano is specifically a hard grating cheese).
Some people don't like the Pecorino Romano; I remember discussing food with my former boss who had grown up in Italy (and even ran for Italian Parliment a few years back), and he thought Pecorino Romano was too salty and strongly flavored to use in risotto. (of course, I make my own stock, so I still needed to add salt from other means).
The only other non-cows milk cheese that I can think of that might work, that's might be easily found would be Manchego Viejo; it's an older varient of Manchego that grates well.
I would've recommended Cheese Net's World Cheese Index, but it looks like the site's gone ... you may have luck through Archive.org's Wayback Machine
The original recipe (in Italian, here a version in English also, at page 7 - warnings, it's a pdf) for pesto alla genovese (Genovese pesto), by Consorzio del pesto alla genovese (Genovese Pesto Consortium), requires both Parmigiano Reggiano - or Grana Padano - (cow's milk cheese) and pecorino (sheep's milk cheese) but in a 3:1 ratio (3 parts of parigiano and 1 part of pecorino). Therefore pecorino (I prefer pecorino romano in this recipe) is required, it cannot be a substitute for a true pesto alla genovese.
I suggest to make a little portion apart with pecorino only for the person with intolerance (pesto alla genovese is quite easy to prepare). But beware: as Joe wrote, pecorino is more salty and strongly flavored than parmigiano.
I agree that using Pecorino Romano is a good and simple solution to this problem. I have also tried goat "Parmesan" which I found tasted really good, and not very goaty. Our local farmers market has a goat farm that sells a wide variety of goatsmilk cheese in types that would normally be made with cows milk, so I am rather lucky.
The other question linked by sarge_smith in the comments covers the common substitutes I can think of (including cow's milk substitutes, despite the question title). They do all tend to be nearly as expensive as parmigiano reggiano, though - in the $10-20/lb range at my grocery store.
So, just in case price is your concern, reggianito is a decent and much cheaper substitute. It's an Argentinian cheese, originally made by immigrant Italians who missed their native cheese. It's not aged as long as parmigiano reggiano, but it's still a nice hard cheese for grating on pasta, or the sorts of recipes you probably have in mind.
Wikipedia says it's often sold in the US as parmesan; I can't really speak to that except to say that I don't think I've ever seen "made in Argentina" on a wedge of "parmesan". My grocery store carries it, though, and it's significantly cheaper than even the cheap US parmesan, let alone the good imported stuff.
Grana Padano or Trentin Grana are both original Italian cheese with similar flavour as long as they are very different for an experienced "user" ...
I'm against other "imitations", specifically born to be exported, being fruited by a less skilled environment and making it think they can be quite the same ... as I said in other similar isuue question, I'm not going to do a religious war, but I can assure "parmesan", "reggianito" and other surrogates are what they are ... surrogates!
BTW, "parmesan" is not "Parmigiano Reggiano" ... the latter is the top quality italian DOP cheese, being different (much flavored) that its sons, Trentin Gana and Grana Padano. Each of these tree products are great original italian cheese, with different characteristics ... everything else is "the same" only in the measure the user don't have the ability to distinguish.
My 2 cents
In my opinion you can generally substitute pecorino romano or grana padano in place of parmesan (parmigiano reggiano). If price is your concern you'll find both those cheeses slightly cheaper than parmesan.
The thenibble.com website has a cheese comparison chart for the Italian hard cheeses.
There is a vendor at my farmer's market with an aged, hard goat cheese that is very similar to parmesan, but that probably won't do you much good. (Unless you're in San Francisco.)
If you aren't being too heavy-handed with the cheese, straight pecorino-romano may work, but the flavor is pretty intense. The stuff I buy tends to be salty, so you'll want to back off on the salt. You might also try aged manchego (manchego viejo), something at least a year old should grate well. Or a combination of manchego and pecorino (in a 2:1 or 3:1 ratio).
If you have a good cheese shop near you, just ask. They're usually run by people with a keen interest in cheese and a lot of domain knowledge.