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To make the dough: In a large bowl or the bowl of a stand mixer fitted with the dough hook, mix together the flour and salt. Add the water in a slow stream and mix to form a shaggy mass with no dry flour remaining, about a minute on medium speed.
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Add the oil and knead until a smooth, elastic dough forms, 12 to 15 minutes by hand or 7 to 10 minutes in the mixer. The dough should feel quite soft but not overly sticky. Cover the bowl and let it rest at room temperature for 20 minutes. While the dough rests, make the filling.
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To make the filling: In a small heatproof bowl, combine the flour, salt, pepper, and five-spice powder.
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In a small saucepan, add the butter, oil, and star anise. Heat over medium until the butter is melted and the mixture is bubbling. Let the mixture continue to simmer for 1 to 2 minutes, or until it's lightly browned around the edges and has mostly stopped sizzling. Discard the star anise.
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Add the butter and oil mixture to the flour mixture and stir to combine, forming a very thin paste.
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To assemble the shou zhua bing: On an ungreased, unfloured work surface, stretch and pat the dough into a 16" x 12" rectangle about 1/8" thick. Spread 3 tablespoons (about 47g) of the filling onto the surface from edge to edge.
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Starting with one long edge, fold the dough in thirds like a letter, forming a rectangle measuring about 16" x 5 1/4". Spread the remaining 2 tablespoons (about 32g) of filling on top of the folded dough.
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Starting with one of the short ends, fold the dough into thirds again, creating a rectangle measuring about 5 1/4" x 4" (about 1 1/2" thick).
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Use a rolling pin to roll the dough into a 12" square (about 1/8" thick). Some of the filling will come out in the process; that’s OK, it can be smeared on top of the dough after it’s rolled.
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Use a knife, pizza wheel, or bench knife to slice the dough into about 24 strips measuring 1/4" in width.
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Starting from one end, gather about 1/4 of the strips and coil them around each other to make a thick spiral measuring about 3" wide and 1" to 1 1/4" tall. Repeat with the remaining dough strips to create four disks. Cover and let them rest at room temperature for 10 minutes.
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Once the dough has rested, use a rolling pin to roll each disk into an 8" round (about 1/8" thick).
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To cook the shou zhua bing: In a 10" skillet, heat 1 generous tablespoon of the vegetable oil over medium heat until shimmering. Carefully place a bing in the pan and cook for about 1 minute. Reduce the heat to medium-low, cover, and cook for about 2 more minutes. The bing should be golden brown around the edges and slightly puffed.
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Brush the surface with a thin layer of oil, flip the bing, cover, and cook for about 2 minutes on the second side.
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Remove the lid, increase the heat to medium-high, and continue cooking for another 1 to 1 1/2 minutes, or until the bing is crispy on the bottom, golden brown all over, and beginning to char in spots on both sides.
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Use tongs or 2 spatulas on opposite sides of the bing to squeeze it briefly to release some steam from within the layers. Transfer to a clean kitchen towel to drain briefly.
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Wipe out the pan with a dry towel and repeat with the remaining dough. Serve shou zhua bing while still hot.
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Storage information: Store leftover shou zhua bing in the refrigerator, covered, for up to 2 days. Reheat in the oven or on the stovetop.
