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Lightly grease a couple of baking sheets, or line them with parchment.
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Whisk together the flour, sugar, baking powder, and salt. Cut the butter into small cubes, and work it into the dry ingredients using your fingers, a mixer, or a fork, mixing until the dough is unevenly crumbly.
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Drizzle in the ice water (or orange juice and water, if you're using whole wheat flour), mixing until the dough is cohesive. Grab a handful; if it holds together willingly and doesn't seem at all dry or crumbly, you've added enough liquid.
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Divide the dough in half, and shape each half into a rough rectangle. Press each of the four sides against your work surface to smooth any ragged edges.
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Wrap the dough, and refrigerate it for 30 minutes. Towards the end of the refrigeration time, preheat the oven to 350°F.
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Take one piece of the dough, and place it on a lightly floured work surface. Roll it into a rectangle that's about 10" x 14", about 1/8" thick. Don't worry about ragged edges; life is imperfect.
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Brush the surface of the dough lightly with some of the beaten egg, then spread half the surface (one of the "long" halves — a swatch about 5" x 14") with 3/4 cup of the currants, pressing them in gently.
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Fold the other half of the dough over the currants, and roll again, until you have a piece of dough about 6" x 15". Some of the currants may pop through; that's OK.
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Brush the dough lightly with some of the beaten egg, and sprinkle with 1/4 cup of the coarse sugar. (If you don't have coarse sugar, use a couple of tablespoons of regular granulated sugar. The cookies won't look as nice, but will taste fine.)
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Now, trim the ragged edges; these will be the "cook's cookies," the ones you spirit away and eat yourself because you don't care what they look like.
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Use a baker's bench knife or a rolling pizza wheel, carefully cut the rectangle of dough into three strips, lengthwise. Then cut each lengthwise strip into five crosswise pieces; you'll have a total of 15 rectangular cookies. Note: Be very careful if you've rolled the dough on a silicone rolling mat; you don't want to cut the mat when you cut the cookies.
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Transfer the cookies to one of the prepared baking sheets, spacing them close together; they won't expand much.
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Repeat the entire process with the remaining piece of dough.
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Bake the cookies for 14 to 18 minutes, until they're a light golden brown. Remove them from the oven, and transfer them to a rack to cool.