Hi, this is my first post here. Just discovered this site.
OK, you've gotten some advice on how to cook a pork shoulder, mostly from an American perspective.
But you said you want a Cuban style sandwich, which means what you actually want to cook is the pork shoulder of Cuba, Puerto Rico and Santo Domingo. That dish is called in Spanish, "pernil." It is very different from American style roast pork, although it uses the same cut of meat.
My SO is Puerto Rican. Not only that, but she grew up in a restaurant that her mother owned. Not only that, but she has spent the last 10 years trying to perfect her pernil even more!
So this is the recipe for Cuban/Puerto Rican/Dominican roast pork shoulder. Please don't be shocked by the excesses of flavor I'm about to describe.
The main thing to remember about C/PR/D pernil is that it is garlicy. Take one to two heads of garlic depending on how much you like garlic. Peel and chop the garlic finely. You can also add a small finely chopped onion or half onion.
To this add about 1 tbs of fresh ground black pepper, 1 tbs kosher salt, 1 tbs garlic powder (or if you have a local Spanish grocery, Goya's Adobo, which is basically garlic powder with extra spices). 1 Tsp of finely ground cumin is also good to add, depending on your taste. Mix this stuff together with olive oil to make a paste.
Now it's time to get medieval on your pork shoulder.
Take a sharp pointy knife and start stabbing the pork shoulder. You want to make holes that you are going to stuff with the paste. Some holes go straight through the skin, some under it, deep into the flesh.
Many non-hispanic cooks think that if you stab the flesh, the juices will run out. This may be true for other cuts, but won't happen with this one, which is so fatty that it's hard to make it come out dry if you cook it slowly.
At this point, if you like a less porky, "cleaner" flavor, you can rinse the pork shoulder in fresh squeezed lemon juice. Pour off the lemon juice when done; you don't want a lemony pork shoulder, just want the acid in the lemon to give the pork a clean flavor.
Now start stuffing the garlic/olive oil paste into the "wounds" of the pork shoulder, really deep into the flesh.
As with the American recipes, you now cook it low and slow, skin side up. 250 at 5-6 hours is about right. It will make a lot of juices, and you should baste the pork shoulder with the juices. This braising will make it incredibly tender and juicy.
Now here is where it becomes again uniquely C/PR/D. When the shoulder done, drain off all the liquid. C/PR/D is actually served kind of dry, and this is the point at which you let the meat get crispy. You don't need to cook it for very long after this. The juice is very garlicy, and diluted with stock, makes good gravy.
When the shoulder is just about done, turn off the oven and put on the broiler on high, with the pork about 6 -12 inches below the fire.
Watch it very carefully. You don't want to ruin all your work at this point by burning it. What you want to do is get the skin to crackle and bubble and for the fat just under it to liquify. In other words, you are making what Americans call "crackling" on the pig.
Take it out. You probably won't want to let it rest. The crackling ("cuero" in Spanish) is so good that your family will fight over it and no one will allow the pig to rest at this point.
Crack off a piece of cuero and hide it for yourself.
Enjoy!
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