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To make the pastry: Combine the flour, cheese powder, salt, and baking powder. Work in the butter until larger, pea-sized clumps form. Drizzle in the ice water and toss, adding more water if necessary to make the dough cohesive.
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Divide the dough in half, and shape each half into a disk. Wrap and refrigerate for at least 30 minutes.
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To make the filling: Stir together the cheese powder, 1 tablespoon of the bagel topping, the melted butter, and water. Set aside.
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Preheat the oven to 375°F.
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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 1/2" to 3" round cutter in the center of the circle, and cut the circle into 32 equal strips, from the cutter to the edge, through all the layers.
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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 tablespoon of bagel topping.
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Bake the pastry for 35 to 40 minutes, until evenly golden brown on top.
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Remove the pastry from the oven and allow it to cool for 10 to 15 minutes before serving.