1. Preheat oven to 350 degrees. Toast pecans on a baking sheet until fragrant and lightly toasted, 8 to 10 minutes. Let cool completely.

2. Grind pecans, sugars, cinnamon, and salt in a food processor until very finely chopped (mixture should resemble very coarse sand).

3. Raise oven temperature to 400 degrees. Place puff pastry sheets side by side on floured parchment; press together at seam to form a 9 1/2-by-18-inch rectangle. Roll out to an 11-by-20-inch rectangle using a rolling pin. Transfer pastry on parchment to a baking sheet. Cover loosely with plastic wrap; refrigerate until firm, about 45 minutes. Brush generously with beaten egg, and evenly sprinkle with pecan mixture, patting it into dough. Starting with a short side, use one hand to roll up as tightly as possible, holding unrolled portion firmly with other palm. Brush off excess flour with a dry pastry brush as you are rolling, and press sides back into shape (they tend to splay). Roll tightly in parchment.

4. Freeze dough until firm, about 20 minutes. Cut crosswise into 1-inch slices. Generously sprinkle a work surface with granulated sugar, and coat both cut sides of dough slices in sugar. Press dough slices to flatten slightly. Roll out into 6- to 7-inch rounds on sugared surface, sprinkling more sugar on top as needed. Place on parchment-lined baking sheets, 3 per sheet; refrigerate until firm, about 30 minutes. Bake in batches until golden brown, 17 to 18 minutes, rotating halfway through. Let cool on baking sheets.