Yes, cavoli means "cabbages," but yes, the sauce uses cauliflower. In Italian the Brassica family terminology tends to be loose, and in Naples, home of this recipe, cavolo is also a synonym of cavolfiore, cauliflower.
Those with absolutely no fear of pork fat can follow tradition and use finely diced lardo in place of the extra virgin olive oil. The hot pepper is optional, but if you do use it, don't spare it: if it's hot, it should be really hot.
In Campania, where this dish is very popular, the cauliflower tends to be green, giving the sauce a lovely green color and a slightly milder, more broccoli-like flavor. Green cauliflowers (not to be confused with the broccolo romanesco, which is similar but not the same) are increasingly available in American farmers' markets, but white will work just as well. Cauliflower and crisp crumbled sausage make for a rustic combination that evokes the Apennines in winter. And in fact the dish is also found in Abruzzo, Lazio, Umbria, and Tuscany. Broccoli and broccoli rabe are also perfect for this sauce.
Pasta shapes: This sauce is typical with strascinati and orecchiette. Other suitable shapes are pizzicotti, fusilli, and sedani or penne. Whatever shape of pasta you use, be sure to cook it in the same water in which you boiled the vegetable.
For the condimento:
To make the dish:
Bring 5 quarts (5 liters) of water to a boil in an 8-quart (8-liter) pot over high heat. Add 3 tablespoons kosher salt, then add the vegetable and boil until just tender. Remove with a slotted spoon and set aside. Reserve the cooking water in the pot for boiling the pasta later.
Put the oil, the garlic, and the piece of chile, if using (but not the red pepper flakes), in a large, deep skillet that will hold all the pasta later. Sauté for a few minutes just until the garlic is golden and the chile has darkened, then discard the garlic and chile. Crumble the sausage meat into the skillet. Brown evenly, stirring, for about 5 minutes.
Raise the heat and add the wine. Let it bubble until the smell of alcohol has disappeared, about 2 minutes. Stir often to keep the meat from sticking. Add the boiled vegetable and mix well. If you are using red pepper flakes instead of a single piece of chile, add them now. Make-ahead note: Everything through this step can can be done earlier in the day.
Bring the vegetable water back to a boil and cook the pasta until al dente.
While the pasta is cooking, reheat the vegetable and sausage over low heat. After the pasta is half done, add a little of its cooking water to the sauce and let it absorb.
When the pasta is al dente, transfer it, dripping wet, with a handheld colander or spider strainer (or the like) to the skillet. Mix well over low heat for just half a minute.
Mix in the cheese and serve immediately, either straight from the skillet or in a warmed serving bowl.
Wine suggestion: Salice Salentino, from Puglia