This is one of my all-time favorite sandwiches. If you want to make this into a full-size sandwich instead of sliders, I recommend adding some sliced ham from the deli. It’s one too many ingredients for a slider, but an essential flavor for an authentic Cuban.
In a blender, combine the vinegar, garlic, salt, pepper, and oregano and blend until smooth. Add the oil and continue blending until the marinade is emulsified.
Pour the marinade into a gallon-size zip-top bag. Add the pork, seal tightly, and make sure it is evenly covered with the marinade. Refrigerate for 2 days.
Remove the pork from the marinade 30 minutes before cooking and wipe the marinade off with paper towels.
Preheat a grill to high or grill pan over high heat. Grill the pork until golden brown and charred on both sides and an instant-read thermometer inserted into the center registers 140°F (60°C). Remove the pork to a cutting board, loosely tent with aluminum foil, and let it rest for 10 minutes before slicing. Slice the pork cross-wise into medallions
Preheat the broiler. Put the bun tops and bottoms, cut-side up, on a baking sheet in an even layer. Mix the mustard and mayonnaise together and spread the mustard mixture on the buns. Divide the cheese among the tops and bottoms. Put under the broiler until the cheese just begins to melt and the rolls are lightly toasted, about 45 seconds.
Place a slice of pork on the bottom rolls and top each with a pickle and
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