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To make the pastry: In a large bowl, combine the flour, cheese powder, baking powder, and salt. Work in the butter until larger, pea-sized clumps form. Drizzle in the smaller amount of ice water and toss to combine, adding more water if necessary to make a cohesive dough that holds together when squeezed.
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Gently fold and knead the dough together to form a cohesive mass. Divide the dough in half (about 275g per piece), and shape each half into a disk. Wrap and refrigerate for at least 30 minutes. The dough can also be made ahead and stored, wrapped in the refrigerator, for up to 2 days.
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To make the filling: Stir together the cheese powder, 4 1/2 teaspoons of the bagel topping, the melted butter, and water. Set aside.
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Preheat the oven to 375°F with a rack in the center.
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Roll one disk of dough into an 11" circle. Place a 10" plate or cake pan on top of the dough, using it as a template to cut out a 10" circle.
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Place the circle on a piece of parchment, and spread the filling mixture evenly over the surface, leaving 1/2" of bare dough around the perimeter.
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Top the filling with an even layer of the grated cheese, again leaving the perimeter bare. Brush the perimeter with the egg wash.
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Roll out and cut the second disk of dough like the first, and place it directly on top of the filling.
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Place a 2 1/4" to 2 1/2" round cutter in the center of the circle. Using a sharp knife or bench knife, cut the circle into 32 equal pieces by cutting from the edge of the round cutter to the outer edge of the circle, all the way through the layers. For easiest results, first cut the circle into quarters, then cut each quarter into 8 equal pieces.
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Remove the cutter from the center of the pastry, and twist each strip three times in the same direction. Transfer the shaped pastry on the parchment to a baking sheet.
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Brush the pastry with the egg wash and sprinkle with the remaining 1 1/2 teaspoons of bagel topping.
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Bake the pastry for 35 to 40 minutes, until evenly golden brown on top. Remove the pastry from the oven and allow it to cool for 10 to 15 minutes before serving.
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Storage information: Store any leftovers airtight at room temperature for up to 2 days; reheat briefly in the oven until warmed through.