Sprinkle 1/2 cup sugar on work surface. Place dough on top and sprinkle with 1/2 cup sugar; press to adhere. Roll out dough into a 16-by-12-inch rectangle, about 1/8 inch thick.

Position dough so that one long side is parallel to edge of work surface. Fold each of the long sides of dough towards the middle to meet one another without overlapping. Sprinkle with 2 tablespoons sugar. Then fold one of the short sides over to meet the opposite short side. Sprinkle with 1 tablespoon sugar. Finally, fold one long side in half to meet the opposite long side. Sprinkle with remaining 1 tablespoon sugar. Firmly press down on dough with your hands, wrap tightly in plastic, and refrigerate at least 1 hour or preferably overnight.

Preheat oven to 450 degrees. Lightly spray a rimmed baking sheet with water. Place more sugar in a shallow bowl. Trim ends of chilled dough, then cut crosswise into 3/4-inch-thick slices. Dip cut sides of slices in sugar, then transfer to prepared sheet, spacing about 3 inches apart.

Bake until sugar is golden and caramelized, 10 to 12 minutes. Using a wide spatula, carefully flip each cookie, then return to oven and continue to bake until deep golden brown, about 6 minutes more. Transfer cookies to a wire rack; let cool completely. Repeat with remaining slices. Cookies are best eaten the day they are made but can be stored in an airtight container, between sheets of parchment, at room temperature up to 1 day.