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Begin by cutting 1/4" butter off the end of each of the 4 sticks in the pound; you'll have about 2 tablespoons butter. Set them (and the remaining butter) aside. You'll be using the 2 tablespoons butter immediately, but won't need the remaining butter until after you've made the dough.
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In a large bowl, whisk together the flour, sugar, yeast, salt, and cardamom. Add the 2 tablespoons cold butter, working it in with your fingers until no large lumps remain. This step coats the flour a bit with fat, making the pastry a tiny bit more tender.
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Add the vanilla, milk, water, and eggs. Mix and knead to make a cohesive, but quite sticky dough. This is easily done in a bread machine set on the dough cycle; or in a mixer. If you use a mixer, the dough won't completely clean the bowl; it'll probably leave a narrow ring around the side, and stick at the bottom.
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Scrape the dough into a ball, and transfer it to a floured work surface. Cover it with plastic wrap, and let it rest for 10 minutes while you prepare the butter.
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Cut each stick of butter in half lengthwise, to make 8 long rectangles. On a piece of floured parchment or plastic wrap, line up 4 of the butter pieces side by side, to form a rectangle. Sprinkle lightly with flour, and cover with another piece of parchment or plastic wrap.
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Gently pound and roll the butter until it's about 6" x 9". The pieces may or may not meld together. If they do, great, they'll be easier to work with. If not, though, that's OK; don't stress about it.
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Repeat with the remaining 4 pieces of butter. You should now have two butter rectangles, about 6" x 9" each.
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Roll the dough into a rectangle about 12" wide and 24" long. Don't worry about being ultra-precise; this is just a guide, though you should try to get fairly close.
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Place one of the butter pieces onto the center third of the dough. Fold one side over the butter to cover it. Place the other butter piece atop the folded-over dough, and fold the remaining dough up over it. You now have a rectangular "packet" of dough-enclosed butter. Pinch the open ends and side closed as best you can.
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Turn the dough 90°, so a 12" side is closest to you. Roll the dough into a 10" x 24" rectangle (approximately). Fold each side into the center; then fold one side over the other to make a rectangular packet about 6" x 10".
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Dust the surface of the dough with flour, wrap it in plastic wrap, and chill in the refrigerator for about 20 minutes.
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Remove the dough from the fridge, and again roll it into a rectangle about 10" x 24". Fold it into a packet as you did in step #10; it'll be about 7" x 12". Roll one final time, fold into a packet, and flour the dough lightly. Wrap loosely (but completely) in plastic, and chill it for 2 hours, or up to 16 hours; we prefer the longer refrigeration, as it gives the dough a chance to relax and rise.
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Before shaping the pastries, select your filling(s). We like to use a variety. Either of the filling suggestions in this recipe make enough to fill all the pastries; so if you want to mix and match, make a half-recipe of the cheese filling, and use only half the amount of fruit filling called for.
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To make the cheese filling, combine all of the ingredients, stirring until smooth. For the smoothest filling, process in a food processor.
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When you're ready to make pastries, remove the dough from the refrigerator, unwrap it, and cut off one-third. You'll work with this piece first; return the remainder to the fridge.
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Divide the dough into 12 pieces. Roll each into a smooth ball, then flatten the balls into 3" to 3 1/2" rounds, making the center thinner than the edges. You want to build up a slight wall of dough all around the circumference; this will help hold the filling. Place the rounds on a parchment-lined or lightly greased baking sheet.
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Working with one-half of the remaining dough at a time, repeat the process; you'll finish with three baking sheets, each with 12 dough rounds.
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Cover the Danish lightly with greased plastic wrap, and let them rise for about 1 hour; they'll become slightly puffy. Towards the end of the rising time, preheat the oven to 400°F.
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Use your fingers to press the centers of the dough rounds as flat as possible, leaving the "sidewalls" puffed. Spoon a slightly heaping measuring teaspoon of filling into the well of each round.
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Brush the exposed edges of pastry with the egg/water topping; this will create a satiny, golden crust.
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Bake the pastries for 15 to 18 minutes, until they're golden brown. Remove them from the oven, and transfer to a rack. Glaze and serve immediately; or wait until they cool, then glaze.
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To make the glaze, whisk the confectioners' sugar and salt with enough water or milk to make a "drizzle-able" glaze.
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Drizzle the glaze atop the pastries. Sprinkle with crushed nuts.