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Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Stir and knead all the dough ingredients together until a soft, smooth, easy-to-handle dough forms. Using a stand mixer equipped with the paddle attachment, this will take about 3 minutes at low speed. Scrape the sides of the bowl halfway through the mix time, adding more flour or water a tablespoon at a time if needed to bring the dough together. The finished dough won't be elastic and springy like a typical yeast dough; it'll feel like cookie dough.
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Place the dough in a lightly greased bowl and allow to rise for 60 minutes. It won’t appear to rise much; it’s OK if it just puffs slightly.
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Divide the dough into two equal pieces and shape each piece into a disk.
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Cover one disk with plastic, and roll the second disk into a 10" circle on a piece of parchment; it helps to use a 10” plate or upside-down pan to trace a circle onto the parchment first. Feel beneath the dough as you roll; if it's sticking to the parchment, pick it up, sprinkle some flour on the parchment, and continue.
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Dust the top surface of the dough circle with flour, then flip it over onto a fresh parchment sheet. This step keeps the dough from sticking as you shape your star.
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Brush the dough with the beaten egg and sprinkle the cinnamon sugar evenly over the surface, leaving 1/4" of bare dough around the perimeter. Set it aside.
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Roll the second piece of dough onto the same piece of parchment with the traced circle, flouring underneath if necessary to prevent sticking. Brush the surface with the beaten egg. Swiftly, using the parchment to help you, turn the dough over onto the filling-covered dough circle, trying to line up the edges as accurately as possible.
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Place a 2 1/2" to 3" round bowl or cup upside-down in the center of the dough circle as a guide. The bowl or cup shouldn't be too heavy and should have a dull edge, as the dough is fairly delicate. With a bench knife or sharp knife, cut the circle into 16 equal strips, from the edge to the cutter, cutting all the way through the two layers.
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Using two hands, pick up two adjacent strips and carefully twist them away from each other 1 1/2 times so that they're standing on edge. Pinch the strips together at their ends. Repeat with the remaining strips of dough to make the eight points of a star. Remove the bowl or cup from the center of the star.
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Transfer the star on its parchment to a baking sheet, cover it with lightly greased plastic wrap, and let it rise until it becomes slightly puffy, about 60 minutes. Again, there won’t be much movement, but you should notice a bit more volume.
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While the star is rising, set a rack in the middle of the oven and preheat the oven to 400°F.
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Brush the star with a thin coat of the beaten egg. Bake it for 17 to 20 minutes, until it's nicely golden; the center should register at least 205°F on a digital thermometer.
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Remove the star from the oven and allow it to cool for about 10 minutes. Dust with confectioners' sugar and serve warm.
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Store the star, tightly wrapped, at room temperature for a day or so, and refresh it in a warm 250°F oven for about 10 minutes before serving. Freeze for longer storage.
