Preheat the oven to 350°F, and spray a roasting pan with nonstick spray.
In a large bowl, toss the potatoes with the apple juice, currants and allspice. Scoop into a single layer in the prepared pan. Pour the extra juices over the top.
Cover the pan with aluminum foil and bake until the potatoes are fork tender, about 30 minutes. Uncover and turn the potatoes. Bake, uncovered, turning once halfway through baking, until the apple juice cooks down and thickens, and the potatoes turn golden, about 20 minutes.