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Using a paring knife, cut a 3-inch wide pocket, about 2-inches deep, into the side of each tenderloin. Season the cavity with salt and pepper. Stuff 1 slice of prosciutto, 1 slice of cheese, and 2 basil leaves into each pocket. Tie 1 piece of kitchen twine at each end and 1 piece in the center of each tenderloin to secure the filling. Season the stuffed tenderloins with salt and pepper.
In a large skillet, heat the oil over medium-high heat, add the tenderloins and sear until golden brown, about 3 minutes per side. Transfer the tenderloins to an oiled baking pan. Roast for 8 to 10 minutes or until the internal temperature registers 150 degrees F on an instant-read thermometer for medium-rare.