How to Make It
Heat oven to 400° F. Place the dried fruit in a medium bowl and add enough boiling water to cover. Set aside to plump, about 10 minutes; drain.
With a sharp knife, cut a slit down the middle of the pork loin parallel to the work surface (do not cut all the way through), then open it like a book. Fill with the dried fruit mixture, close the loin, and tie with kitchen twine.
Heat 1 tablespoon of the oil in a large skillet over medium-high heat. Season the pork with 1 teaspoon salt and ½ teaspoon pepper. Cook, turning occasionally, until browned on all sides, 5 to 6 minutes.
Meanwhile, on a rimmed baking sheet, toss the carrots, parsnips, and turnips with the rosemary, the remaining 3 tablespoons of oil, 1 teaspoon salt, and ½ teaspoon pepper.
Nestle the pork in the vegetables, transfer to oven, and roast, tossing the vegetables occasionally, until they are tender and the internal temperature of the pork registers 145° F, 35 to 40 minutes. Let rest for 10 minutes before slicing. Serve with the vegetables and any pan drippings.