For the pickles: Combine the vinegar, dill, sugar, salt, coriander and mustard in a medium saucepan. Bring to a boil over high heat and cook until the sugar and salt are dissolved. Remove from the heat and let cool for 15 minutes. Put the cucumbers in a medium bowl, pour the pickling liquid over, cover the bowl and refrigerate for at least 30 minutes and up to 24 hours.
For the sour orange glaze: Combine the orange juice and lime juice in a small nonreactive saucepan over high heat and cook until reduced to 1/2 cup, about 20 minutes. Whisk in the honey and vinegar and season with salt and pepper. Let cool slightly.
For the pork: Preheat the oven to 425 degrees F. Season the pork with salt and pepper and rub with the steak rub. Let sit for 15 minutes at room temperature.
Heat the oil over high heat in a cast-iron pan or oven-proof skillet until it begins to shimmer. Add the pork and cook until a crust has formed on all sides, about 2 minutes per side. Brush liberally with the sour orange glaze and transfer the pan to the oven. Brush with the glaze every few minutes, and cook until an instant-read thermometer inserted into the center of the pork registers 145 degrees F, about 10 minutes. Remove the pork to a cutting board and let rest for 10 minutes before slicing. Slice the pork thinly.
For the garlic mayonnaise: Combine the mayonnaise, mustard, oregano, garlic, salt and pepper to taste in a small bowl. Whisk together and let sit at room temperature for at least 15 minutes to allow the flavors to meld.
For the serrano ham: Heat the oil in a small saucepan until it reaches 350 degrees F. Add the ham one slice at a time and cook until crisp, about 30 seconds. Drain on a plate lined with paper towels.
To serve: Spread the top and bottom of each bun with the garlic mayonnaise and top each piece with 2 slices of cheese. Put some pickles on the bottom piece of bun. Top with 4 to 5 slices of the pork and 2 slices of the fried ham. Combine the tops and bottoms to make the sandwiches.
Brush the outsides of the buns with the butter. Heat a cast-iron pan over low heat. Put 2 sandwiches in at a time, top-sides down, and press with a brick wrapped in foil, or put foil over the top of the sandwiches and weigh them down with another heavy cast-iron pan. Cook until the bread is crispy, then flip over and continue cooking until the bottom is crispy and the cheese has melted, 6 to 8 minutes total. Slice in half and eat.
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