For the mustard aioli: In a bowl, combine the mayonnaise, mustard, lemon zest, horseradish, dry mustard, salt, hot sauce, garlic and lemon juice. Mix well. Cover and refrigerate until ready to use.
For the Cubano sandwich: Preheat the oven to 350 degrees F.
In a bowl, mix together the paprika, cumin, dry mustard, onion powder, celery salt, kosher salt and brown sugar. Rub the pork tenderloin all over with the spice rub. Transfer to a baking sheet and roast to an internal temperature of 165 degrees F, about 25 minutes.
Remove the pork from the oven and let rest for 10 minutes. Slice thin and set aside.
Heat a large skillet over medium-low heat. Add the pancetta slices in batches and cook until crispy. Drain on a paper-towel-lined plate. Set aside.
To assemble: Slice a loaf horizontally. Spread the cut sides with 2 tablespoons mustard aioli, then spread the bottom half with 2 teaspoons relish. Top with 1/2 cup of the shredded Gruyere, 5 to 7 slices of the pork tenderloin, 3 slices pancetta and then another 1/4 cup of the Gruyere.
Heat a griddle pan over medium-high heat until hot. Spread 1 tablespoon of the mayo on the exterior of the bread. Place the sandwich in the pan and press firmly with a panini press or heavy skillet. Heat until the bread has toasted and the cheese is melted, 5 to 7 minutes. Remove from the pan, slice in half and serve. Repeat for the remaining sandwiches.