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In a blender purée figs and dates with water and 2 tablespoons refined sugar. In a bowl, whisk together flour, anise, baking powder, baking soda, and salt. In another bowl with an electric mixer beat together butter, cream cheese, and remaining 1/2 cup refined sugar until light and fluffy. Add vanilla, yolk, and flour mixture and beat until a dough forms. Form dough into a disk. Chill dough, wrapped in wax paper, 1 hour, or until firm enough to handle.
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On a lightly floured sheet of wax paper with a floured rolling pin roll out dough into a 13- by 10- inch rectangle, about 1/3 inch thick. Drop fig mixture by spoonfuls onto dough and gently spread an even layer over dough. Starting with a long side, roll dough jelly-roll fashion into a 13-inch log, using wax paper as a guide. Roll log in raw sugar to coat. Chill log, wrapped in wax paper, 4 hours, or until firm.
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Preheat oven to 350° F. and lightly butter 2 baking sheets.
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Cut log into 1/3-inch-thick rounds and arrange about 2 inches apart on baking sheets. Bake cookies in batches in middle of oven until pale golden, about 13 minutes, and transfer to racks to cool. Makes about 36 cookies.
