Combine the pecans, sugars, cinnamon and salt in the bowl of a food processor. Pulse until the mixture is very finely chopped and resembles coarse sand.
On lightly floured parchment paper, roll the puff pastry out into an 11 x 20-inch rectangle (or close – doesn’t need to be exact).* Transfer the rolled out pastry on the parchment to a baking sheet, cover loosely with a clean kitchen towel, and refrigerate until firm, about 45 minutes.
Remove the dough from the fridge. Brush the dough evenly with the beaten egg. Sprinkle the pecan-sugar mixture evenly over the top, pressing gently into the dough. Starting with the short side of the dough, roll up into a spiraled log to enclose the filling (basically the same as the technique in this post). Roll the log tightly in parchment or plastic wrap and freeze until firm, about 20 minutes.
Preheat the oven to 350˚ F. Use a sharp serrated knife to cut the dough into slices about ¾-inch thick. Generously sprinkle a work surface with sugar (or cinnamon sugar – your call). Use a rolling pin to roll each slice to a diameter of about 6 or 7 inches, adding more sugar as needed to prevent sticking. Place the rolled cookies on parchment lined baking sheets, 3-4 per sheet. Refrigerate for 30 minutes.
Bake, rotating the pans halfway through, until the cookies are light golden, about 18 minutes. Let cool on baking sheets slightly. Carefully transfer to a wire rack and let cool before serving.
*If using sheets of pre-made puff pastry, press two sheets together and pinch at the seam. Then roll out as directed.