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1. Thaw the puff pastry in the refrigerator if frozen, then let it sit at room temperature until just pliable but still cold. Line a baking sheet with parchment paper.
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2. Preheat the oven to 400 F (200 C).
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3. Melt the unsalted butter gently in a small saucepan or in short bursts in the microwave until just liquid but not sizzling.
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4. In a bowl, whisk together the granulated sugar, unsweetened cocoa powder, orange zest, orange juice, vanilla extract, salt, and the melted butter until you have a smooth, spreadable paste. If it seems too thick, add a few drops of orange juice; if too thin, whisk in a little more cocoa powder.
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5. Lightly flour your work surface if needed and unfold the puff pastry into a rectangle. With a rolling pin, gently roll it out to smooth the seams and slightly enlarge it, keeping the rectangle shape.
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6. Spread the cocoa-orange paste evenly over the puff pastry, leaving a slim border along one long edge for sealing.
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7. Starting from the long edge opposite the clean border, roll the pastry up tightly into a log, keeping the roll even. Pinch the seam along the border to seal, then place the log seam-side down.
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8. Transfer the log to a cutting board and chill it in the refrigerator for about 10 minutes so it firms slightly and is easier to slice.
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9. In a small bowl, whisk together the egg and water to make an egg wash.
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10. Using a sharp knife, slice the chilled pastry log into 12 even rounds and arrange them cut-side up on the prepared baking sheet, spacing them slightly apart to allow for puffing.
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11. Brush the tops and sides of each pinwheel lightly with the egg wash.
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12. Bake the pinwheels for 15 to 18 minutes, or until puffed and deep golden brown with the filling bubbling slightly. Rotate the tray halfway through baking for even color.
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13. Remove the baking sheet from the oven and let the pinwheels cool on the tray for 5 minutes, then transfer them to a wire rack to cool until just warm or room temperature.
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14. In a small bowl, whisk together the powdered sugar, orange juice, and orange zest until smooth and thick but pourable. If needed, adjust with a few drops more juice or a bit more powdered sugar to reach drizzling consistency.
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15. Drizzle the orange glaze over the cooled or slightly warm pinwheels and let it set for a few minutes before serving.
