In honor of National Rum Day today, we’re mixing a mojito and making these smoky Cuban sandwiches! Traditional Cuban sandwiches call for slow-roasted pork shoulder, but a smoked pork loin cooks more quickly and makes a sandwich that’s just as tasty.
Cuban Sandwiches with Slow-Smoked Pork Loin
1⁄2 cup sour orange juice or 1⁄4 cup each fresh orange juice and fresh lime juice, combined
1 boneless pork loin roast, about 3 lb.
5 cloves garlic, finely chopped
1 tsp. cumin
1 tsp. dried oregano
Kosher salt and freshly ground pepper
About 8 cups wood chips, soaked in water for 30 minutes
8 hoagie or soft French rolls, split
Yellow mustard for spreading
1⁄2 lb. ham, thinly sliced
Dill pickle chips for serving
1⁄2 lb. provolone or Swiss cheese, sliced
Load a marinade injector with the orange juice and inject the juice into the pork in several places. In a small bowl, stir together the garlic, cumin, oregano, 1 1⁄2 teaspoons salt, and 1⁄2 teaspoon pepper. Rub the mixture evenly over the pork loin. Place the loin in a large lock-top plastic bag, seal the bag closed, and refrigerate for 24 hours.
At least 30 minutes before you plan to start grilling, remove the pork loin from the refrigerator, and remove it from the plastic bag.
Prepare a charcoal or gas grill for smoking over medium heat; the temperature inside the grill should be 350º–375ºF. If using charcoal, bank the lit coals on either side of the grill bed, leaving a strip in the center without heat. Place a drip pan in the center and fill the pan with water. Add half of the wood chips to the fire just before grilling. If using gas, fill the smoker box with wood chips, then preheat the grill. Turn off 1 or more burners to create a cooler zone. Brush and oil the grill grate.
Place the pork on the grill over the direct-heat area and sear, turning as needed, until nicely browned on all sides, about 10 minutes. Move the pork roast to the indirect-heat area, cover, and cook for about 1 hour, or until an instant-read thermometer inserted into the thickest part of the loin registers 145ºF, adding the remaining wood chips after about 30 minutes.
Transfer the pork loin to a cutting board, tent with aluminum foil, and let rest for about 10 minutes. If using a charcoal grill, spread the coals out evenly over the fire bed. If using a gas grill, turn the burners to high.
Coat the cut sides of the rolls with the mustard. Evenly divide the ham among the rolls, and then top with some of the pickles. Slice the pork thinly, and place some of the pork slices over the pickles. (You will have leftover pork; it will keep in the refrigerator for 1 week.) Top with the cheese slices. Place the sandwiches on the grill over direct heat. Using a long spatula, press down on each sandwich until the cheese melts, 2–3 minutes. Serve at once. Serves 8.