Preheat oven to 375 degrees F (190 degrees C).
Remove the flap of meat at the wider end of the tenderloin and trim the last two inches off of the narrow end of the tenderloin; chop trimmings and reserve.
Cut from one side of the tenderloin through the middle horizontally to within one-half inch of the other side. Open the two sides and spread them out like an open book. Cut a few shallow slashes in the meat. Cover the meat with plastic wrap and pound to about 1/2-inch thick. Roll up pounded tenderloin, cover with plastic wrap, and refrigerate to keep cold.
Mix chopped pork trimmings, parsley, bread crumbs, currants, garlic, rosemary, egg, olive oil, 2 teaspoons salt, 1 1/2 teaspoons black pepper, and cayenne pepper together in a bowl with a fork until stuffing is well-combined.
Unroll tenderloin on work surface. Spread stuffing over tenderloin, leaving a 2-inch border on one of the long-sides. Roll up tenderloin, ending at the 2-inch border; tie meat with twine to secure shape. Season tenderloin all over with salt and black pepper.
Heat an oven-safe skillet over high heat until hot. Cook tenderloin in hot skillet until browned, 3 to 4 minutes per side.
Cook in the preheated oven until pork is slightly pink in the center, about 30 minutes. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C). Transfer to a plate and let rest for 15 minutes before removing twine and slicing.
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