Preheat oven to 350°F. Combine paprika, cumin, and chili powder. Coat pork tenderloin generously with the spice mixture. In a hot cast-iron skillet, sear pork on all sides. Transfer entire pan to oven and cook for about 20 minutes. Let rest before slicing.
Steam buns in a bamboo steamer for about 5 minutes.
In a small bowl, combine all ingredients for the cilantro-lime mustard.
In a skillet lightly coated with oil, add two slices of ham. Top each with a slice of Gruyère, another slice of ham, another piece of cheese, and another piece of ham. Spread cilantro-lime mayo over the top, then cover the pan and allow cheese to melt, about 3-5 minutes.
Place the meat and cheese stack in a warm bun, then top with sliced pork, mustard, more cheese and pickles.
Torch the outside to give the bun a crunchy, crust-like finish.