Preheat the oven to 375 degrees F (190 degrees C).

Remove flap of meat at wider end of tenderloin and trim last 2 inches off narrow end; chop trimmings and reserve.

Place tenderloin with a short end toward you. Cut into tenderloin with knife parallel to cutting board about 1-inch from bottom (in the middle) along entire length of one long edge; continue cutting stopping about 1/2-inch from other long edge, without cutting all the way through. Open tenderloin like a book.

Cut a few shallow slashes in the flattened meat, being careful not to cut all the way through. Cover flattened tenderloin with heavy plastic; pound with the smooth side of a meat mallet to about a 1/2-inch thickness. 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 edges. Roll up tenderloin, ending at the 2-inch border; tie with twine to secure shape. Season tenderloin on all sides with salt and black pepper.

Heat an oven-safe skillet on stovetop over high heat until hot. Add tenderloin; cook until browned, 3 to 4 minutes per side.

Cook in the preheated oven until tenderloin 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).