For the braised pork shoulder: Preheat the oven to 300 degrees F.
Combine the salt, pepper, oregano and cumin, and mix well. Rub the pork all over with the spice mix.
Heat a large cast-iron skillet or saute pan over high heat until smoking. Add the oil and sear the pork on all sides until well browned, 3 to 4 minutes per side. Transfer to a deep baking dish.
Deglaze the skillet with the chicken stock, then pour enough stock over the pork to cover by two-thirds. Cover tightly with parchment paper and then with foil. Place in the oven and cook until the pork reaches an internal temperature of 190 degrees F, 2 1/2 to 3 hours.
Remove from the oven and allow the pork to cool in its cooking liquid for about 30 minutes. When cool, slice the pork thin and against the grain.
For the Cuban sandwich: Heat a flat top grill or panini press to medium-high.
Cut the bread in half horizontally and spread 1/2 tablespoon of butter on each cut-side. Toast the bread, cut-side down. (If using a panini press, do not close the press.)
Cut the swiss cheese slices in half; place two halves on bottom halves of the bread. Layer with 6 ounces of sliced pork shoulder, 4 ounces of sliced ham, 2 pickle slices and 2 half slices of swiss cheese. Spread 1 tablespoon of Dijon mustard on the top piece of bread, and top the sandwich.
Brush the top and bottom of each sandwich with butter and place on the flat top with a weight on top, or use a panini press. Cook until golden brown and the cheese is melted; on a flat top, turn the sandwich over and cook until the reverse side is crisp and golden.