COMBINE sultanas with currants, peel, orange zest, brown sugar and spices in a medium bowl. Stir in brandy and amaretto. Microwave on high 3 min, stirring halfway through, or let mixture stand for 15 min. Scrape into a food processor. Whirl until puréed, scraping down sides as needed.
POSITION oven racks in top and bottom thirds of oven. Preheat to 400F. Line 2 large baking sheets with parchment.
UNROLL cold puff pastry sheets. Divide mincemeat between pastry sheets. Spread in an even layer to the edges. Tightly roll opposite ends of each sheet to the centre until they meet. Freeze logs on a baking sheet until just firm, about 20 min.
REMOVE 1 log from freezer and slice into 1/4-in. slices. Press a cut side into coarse sugar. Arrange cookies, sugar-side up, on prepared sheets about 1 in. apart.
BAKE in top and bottom thirds of oven, switching sheets halfway through, until golden brown and crisp, 16 to 18 min. Transfer to a rack to cool completely. Repeat with remaining log. Store cookies in an airtight container up to 1 week or freeze at least 1 month. (Prep tip: If using a block of puff pastry dough, roll out dough to a 10-in. square.)