Line several baking sheets with parchment paper. Combine 1/2 cup of the sugar and the cinnamon in a small bowl. Dust work surface with a tablespoon or two of cinnamon-sugar. Roll out puff pastry on the sugar to 12 x 9 inches.

Brush dough with the beaten egg. Sprinkle cinnamon-sugar mixture over dough, patting it lightly so that it adheres. With the tip of a paring knife, mark a line (but do not cut through) lengthwise down center of dough. Fold long sides of the rectangle toward the center, leaving 1/3 inch uncovered on either side of the line. Then, fold one side of dough over the other; you will have a total of four layers. Wrap in plastic; freeze until firm, at least one hour and up to 2 weeks.

Heat oven to 400 degrees F. Unwrap pastry, and cut into 1/3- to 1/4-inch-thick slices. Arrange slices, cut-side down, 1-inch apart on prepared baking sheets. Bake until golden brown, 12 to 14 minutes. Cool on the baking sheets for 15 to 20 minutes and serve at room temperature. Keep at room temperature in an airtight container for up to 3 days.