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To make the Cuban braised pork:
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Place the onions and garlic cloves into a large heavy pot.
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Place the pork shoulder on top of the onions.
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Pour 3 tablespoons of the vinegar over the top of the pork and then sprinkle the pork with the oregano, salt and red pepper flakes.
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Fill the pot half way full of water, put a lid on it and set the pot over medium heat.
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After 10 minutes, lower the heat to low.
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Simmer the pork for about 1 1/2 hours.
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Then take the lid off, and flip the pork to cook it evenly.
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Add the rest of the vinegar and put the lid back on it.
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Cook for another 60-90 minutes.
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Remove the pot from the heat and pull the pork out of the pot.
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Put the pork on a work surface or cutting board.
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Remove the strings from the pork (if there were strings) and shred the pork (using two forks or your hands).
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Be sure to remove the fat and any connective tissues that still remain.
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Discard that!
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Move the pork to a bowl or storage container.
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If you are not going to use this right away (or maybe not all of it at once) then ladle a cup or two of the braising liquid over the pork and store the meat in the liquid.
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Make sure to season it with a little kosher salt if the meat needs it.
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To make the sandwich:
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Preheat a sandwich press or grill pan.
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Slice the roll in half horizontally.
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Spread yellow mustard over both sides of the bread.
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Pile the Swiss cheese onto one side of the bread.
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Add the smoked ham.
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Add several large spoons full of the pulled pork.
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Add bread and butter pickles and top the sandwich with the other slice of bread.
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Grill or cook in a sandwich press until golden and the cheese is melted.
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Slice in half and enjoy hot with extra pickles!
