Remove dough from refrigerator onto a lightly floured work surface. Divide into four equal portions. Shape each into a ball, then flatten to form disks. Roll one disk out to a rough 6 inch circle by rolling out from center, lifting and turning dough, and occasionally flipping to prevent sticking. Flour board as necessary. Place on cookie sheet lined with parchment or plastic wrap and place another sheet of parchment or wrap on top. Roll out second ball of dough in same manner. Repeat with remaining dough. Refrigerate at least 30 minutes, or until ready to assemble tarts. Preheat oven to 425 degrees. Combine rum and raisins in a small saucepan and heat over low medium flame until rum simmers. Turn off heat and let steep while you prepare the apples. Peel the apples, cut them in half, and core them. Cut each half into six even wedges. In a large skillet, melt the butter over medium high heat. When it has stopped foaming, add the apples and toss well. Sprinkle sugar, cinnamon, cloves and allspice over the apples and toss. Lower heat to medium and continue to saute 10-15 minutes until apples are lightly browned. Add steeped raisins with any remaining rum, along with the lime juice, and cook until liquids have evaporated. Remove from the heat and let cool.

Take dough circles out of refrigerator and place before you on the board. Brush each lightly with beaten egg. Arrange 12 apple wedges on center of each dough round in a pinwheel pattern., leaving a 1 inch border all around. Spoon remaining raisins over the apples. Fold edges of dough up over apples, in overlapping fashion. Brush dough with egg wash and sprinkle apples with brown sugar. Bake until golden brown, about 20 minutes. Serve

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