Preheat oven to 375°. Line a 15x10x1-inch baking pan with foil and brush with 1 tablespoon of the oil; set aside. Slice the pork in half lengthwise, cutting to but not through the other side. Spread open and flatten with your hands. Spread applesauce evenly over pork. Top with raisins. Close the roast back up and secure with toothpicks or tight with 100% cotton kitchen string.
Place pork, seam side down, in prepared pan. Drizzle with remaining oil and season with salt and pepper. Roast the pork, uncovered, about 35 minutes or until a meat thermometer registers 145°F. Remove from oven. Cover with foil and let stand 10 minutes.
Meanwhile, place potatoes in a large saucepan and cover with water by 1 inch. Bring to boiling, reduce heat, and simmer, covered for 15 to 20 minutes or until potatoes are tender. Drain and return to pan. Add butter and mash with a potato masher, adding broth to desired consistency. Season with additional salt and pepper.
Remove toothpicks or string from pork. Slice roast to serve. Serve with potatoes and garnish with parsley.