Brussels sprouts and cured pork go together like power saws and safety glasses, or onigiri and miso soup, or open-toed shoes and all-the-time.* They're perfect partners, and humans have been cooking bacon and Brussels sprouts together ever since the first time they cooked bacon and Brussels sprouts together.
This may apply just to me.
But I do like to mix things up from time to time. Sometimes I wear my fashionable orange safety glasses, or put pickled plums in my onigiri, or swap out my sandals for flip-flops. Similarly, sometimes I trade in the bacon for chorizo.
If you want your Brussels sprouts with chorizo to be the best Brussels sprouts with chorizo they can be, it's important to start with the right chorizo...and not all chorizo is the right chorizo.
The problem is that the word "chorizo" is broad. It can refer to a wide range of products, from crumbly and vinegary, warm-spice-scented Mexican chorizo, to garlicky, fermented Colombian chorizo, to dry-cured, raw Spanish-style chorizo. For this recipe, the Spanish stuff is what you're after. If the chorizo you're looking at is soft and fresh-feeling, pass it by. If it says "fully cooked" anywhere on the package, definitely skip it. Spanish chorizo will look more like a stick of pepperoni or salami than a fresh sausage. (If you can't find it locally, you can always order it online.)
Once you've got the chorizo in your hands, the rest of the recipe is a cakewalk. I start by chopping the chorizo and sautéing it in some extra-virgin olive oil (which, by the way, is a perfectly reasonable thing to do, despite what some naysayers say).
Spanish chorizo is seasoned with smoked paprika and garlic, plus it's fermented, so it packs a powerful punch. The goal is to get that flavor into the olive oil, which we'll in turn use to flavor the sprouts. On the other hand, the chorizo will get tough if it's cooked too long. The trick is to start the chorizo and the oil in a cold pan and gently warm it up, stirring as you do so. Once the sausage is just starting to crisp, add shallots and garlic to the pan and sauté them gently before reinforcing the flavor with a couple of extra teaspoons of paprika.
If I were to simply toss this mixture with the Brussels sprouts and throw them in the oven, the aromatics and chorizo would burn by the time the sprouts were nicely charred. Instead, I strain the oil onto the sprouts, reserving the chorizo and other solids while I roast them.
Sprouts are best roasted at very high heat—450°F (230°C)—in order to char the outsides before the insides turn completely mushy. This takes just about 20 minutes or so. Once they're out of the oven, I transfer them to a bowl and add back the chorizo/shallot/garlic mixture, along with a little dash of sherry vinegar (acid is just as important as salt in cooking!) and just a touch of honey. That sweetness balances out the tartness from the vinegar and the spice from the chorizo and paprika.
Please, make sure you've put on the proper safety equipment before you begin eating.