Besides ragù alla napoletana, la genovese is probably the most iconic of all Neapolitan pasta sauces, and yet it is little known outside Italy or, for that matter, little seen outside Naples itself. And, for reasons I cannot quite figure out, it did not seem to survive the trans-Atlantic voyage; in my experience, la genovese does not form part of the Italian-American repertoire. All of which is really a shame, because this has got to be one of the most delicious sauces ever devised for dressing pastasciutta.
La genovese requires long, slow cooking but can simmer unattended for most of the time. You cover the bottom of a large pot, preferably either terracotta or enameled cast-iron, with a generous amount of olive oil or, if want true authenticity, melt a heaping wad of lard. I usually compromise and melt just a spoonful of lard in olive oil to give it that special savory flavor. Then add lots of finely chopped onion to the pot (see below for measurements) along with a carrot and a stalk of celery, both chopped finely as well. Then add a nice, large piece of stewing beef—my favorite is chuck, for its rich flavor—and some finely chopped bits of salumi (salame, pancetta and/or prosciutto) along with a glassful of white wine or water. Season the ingredients well with salt and pepper, cover and allow this mixture to simmer over very low heat for about 3 hours, uncovering the pot and stirring from time to time, and adding a bit of water if needed to keep the mixture moist, until the meat is fork-tender and the onion is well reduced and melted into a kind of 'cream'.
At the last, raise the heat and allow the onions to caramelize until they are nice golden brown color—but be sure not to burn them. Remove the beef for another use, possibly as a second course. The remaining onion cream is your sauce. Use the onion sauce to dress ziti or other stubby pastas. If you like, serve with grated parmesan or pecorino cheese. (I prefer the former over the latter.)
Measurements: To make enough genovese to dress pasta for 4-6 people, use 1.5 kilos (3 lbs.) of onions. Recipes range in the ratio of meat to onion, from almost 1:1 (usually a bit less meat than onion) to 1:2, with most calling for 1:1.5, so for four-six people, add 1 kilo (2 lbs.) of meat. Use just a bit of the salumi, perhaps 100 grams (3-1/2 oz.)
NOTES: The most common variation of this dish, much used for an everyday version of la genovese, is to omit the beef and simply use the bits of salumi to provide savor to the onions (it's a good use for any spare bits that may be hanging around your fridge) or even no meat at all. Either of these versions can be called la finta genovese or 'mock genovese'. Some recipes call for a bit of tomato purée or paste towards the end, by the original—and my preferred—version is in bianco. Some versions also call for adding a great deal of water, enough to immerse the meat, and letting it reduce over time, rather than adding it bit by bit, using the so called arrosto morto technique.
The typical pasta, as mentioned, is ziti, especially the long type that you break into sections by hand (pictured in the post on zitoni al forno) but another stubby pasta like penne would also do. I have seen recipes calling for bucatini, also know as perciatelli, a kind of thick, hollow spaghetti that is popular in both Naples and Rome (and is indispensible to make the Roman classic bucatini all'amatriciana).
You may have cottoned on to the fact that genovese means 'from Genoa'. So why is this name for a typically Neapolitan dish you may ask? Well, no one really knows for sure, but the most popular story has it that it was invented by Genovese merchants living in Naples in the 16th century. When they left, their chefs stayed behind and started cooking the dish for the natives. The original version, as detailed by the estimed gastronome Ippolito Cavalcanti in the 19th century, was more like a typical French daube, a meat dish braised in a mirepoix. Somewhere along the line, the onions became the star of the show, and the dish was transformed from a secondo to a primo. (This article gives some interesting details, along with another recipe for the dish.)