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1
Pour the lukewarm milk into a small bowl. Add the yeast and the 1/4 cup of flour and whisk until smooth. Cover with plastic wrap and leave in a warm place until the mixture gets puffy and active, at least 15 minutes.
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2
Meanwhile, in the bowl of a stand mixer fitted with the dough hook attachment, combine the remaining 2 1/2 cups flour, the sugar, and the salt. Add the eggs and the room-temperature milk to the bowl and knead on low speed until the dough is a smooth mass (it may not form around the dough hook), 5 to 8 minutes.
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3
While the dough is kneading, cut the butter into about 12 pieces. With the machine running on low, gradually add the butter, a few pieces at a time, until thoroughly incorporated. Continue kneading on low for about 8 minutes. The dough may still not form around the dough hook. Scrape the dough off the dough hook and add the yeast mixture. Knead on low speed until the dough feels smooth and elastic, yet still fluffy and soft, about another 10 minutes. It will remain sticky.
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4
On a lightly floured work surface, shape the dough into a ball, dust a large bowl lightly with flour, and add the dough. Cover the bowl with plastic wrap and leave in a warm place to rise until doubled in size, about 2 hours. When ready, the dough will not spring back when poked gently with a finger.
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5
Punch the dough down and turn it out onto a lightly floured work surface. Cut the dough into 12 evenly sized pieces (about 2 1/2 ounces each). Under cupped palms with stiff fingers, roll the pieces into tight balls. They should stick a little bit to the counter to create tension, so use very little to no flour on the countertop. Cover with a kitchen towel and let rest for about 15 minutes.
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6
To shape the bretzels, work sequentially, completing each step with all the dough. This allows the dough to rest and makes it easier to work. As you work, if the dough seems to fight you and doesn't stretch out, just let it rest for a few minutes and then continue. Line 2 baking sheets with nonstick baking mats or parchment paper.
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7
Preheat the oven to 350u00b0F. Roll each ball into a log about 6 inches long. Then roll each of these into a long, thin rope about 30 inches long, tapering the ends to points, and immediately shape it and arrange it on the prepared baking sheet.
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8
To make the classic twisted pretzel shape, pick up the tapered ends of the 30-inch-long roll and cross your hands, right over left. The end that was on the right is now on the left. Repeat for a second twist. To complete the classic pretzel shape, lift the tapered ends and drape them over the sides of the bretzel, at 10 o'clock and 2 o'clock. You can leave the tips on top or flip the bretzel over, covering the ends with the sides of the bretzel. Either is correct. Your finished bretzel should be about 5 inches wide with very large openings to fill the pastry cream.
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9
Meanwhile, scrape the warm pastry cream into a pastry bag fitted with a large round tip. As soon as you have shaped a bretzel, pipe the pastry cream into the open spaces of the bretzels, overfilling them so the cream mounds above the dough. This helps prevent the dough from springing back on itself. With a wet finger, smooth any points left by the piping. Set the bretzels aside in a warm place to rise, about 30 minutes.
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10
In a small bowl, whisk the egg yolk with 1/2 teaspoon water. With a pastry brush, brush the dough only with the egg wash. Bake until medium brown, about 20 minutes, rotating the pans front to back and top to bottom about halfway through. Let the bretzels cool for a few minutes on the baking sheets.
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11
Mix the powdered sugar in a bowl with just enough water to make a thin sugar glaze and brush it onto the breads. Let the bretzels continue to cool on the baking sheets until the pastry cream has firmed up. I like them best still warm from the oven (a privilege of living above a pastry shop), but they taste very good for the whole day.
