These pretty little cookies are similar to the bakery staples, but made with a flaky, homey, easier version of puff pastry. A liberal sprinkle of cinnamon and sugar in between the layers gives each cookie both sweetness and a hint of spice.
1 1/4 cups all-purpose flour
1 teaspoon salt
1 1/2 sticks unsalted butter, frozen
5 to 6 tablespoons ice water
1 cup sugar
2 teaspoons cinnamon
Stir together flour and salt in a chilled large metal bowl. Coarsely grate frozen butter into flour, gently tossing to coat butter.
Drizzle 5 tablespoons ice water evenly over flour mixture and gently stir with a fork until incorporated. Test mixture by gently squeezing a small handful: When dough has the proper texture, it will hold together without crumbling apart. If necessary, add another tablespoon water, stirring until just incorporated, and test again. (Do not overwork dough or add too much water, or pastry will be tough; dough will be lumpy and streaky.)
Form dough into a 5-inch square, then chill, wrapped in plastic wrap, until firm, at least 30 minutes.
Roll out dough on a floured surface with a floured rolling pin into a 15- by 8-inch rectangle (with a short side nearest you). Brush off excess flour and fold dough into thirds like a letter. Rewrap dough and chill until firm, at least 30 minutes.
Arrange dough with a short side nearest you on a floured surface and repeat rolling out, folding, and chilling 2 more times. Brush off any excess flour, then halve dough crosswise with a sharp knife and chill, wrapped separately in plastic wrap, at least 1 hour.
Stir together sugar and cinnamon, then generously sprinkle a clean work surface with some of cinnamon sugar and place 1 piece of chilled dough on top. Quickly roll out into a 16- by 12-inch rectangle (1/8 to 1/16 inch thick; if dough becomes too soft, chill on a baking sheet until firm). Trim edges with a sharp knife. Sprinkle top of dough evenly with some cinnamon sugar to cover completely, brushing off any excess. Fold 2 opposite long sides of pastry so they meet in center. Fold in same sides of pastry in same manner, then fold one half over the other (like a book) and press gently with a rolling pin to flatten slightly, forming a long rectangular log. Sprinkle with additional cinnamon sugar if dough is sticky.
Chill on a baking sheet, uncovered, until firm, at least 30 minutes and up to 2 hours. Meanwhile, repeat with remaining piece of dough and cinnamon sugar.
Preheat oven to 425°F with rack in middle. Line a large baking sheet with parchment paper.
Cut 1 log of dough crosswise into 1/4-inch-thick slices with a sharp knife and arrange slices, cut sides down, 1 1/2 inches apart on baking sheet. Bake until puffed and golden around edges, 7 to 9 minutes. Remove from oven and turn palmiers over with a spatula. (If palmiers begin to unroll, gently press to reshape when cooled slightly.) Continue baking until golden all over and sugar is caramelized, 3 to 5 minutes more. Transfer as done (palmiers may not bake evenly) to a rack and cool. Make more cookies on cooled baking sheet lined with fresh parchment.
Dough, without cinnamon sugar, can be chilled, wrapped well, up to 2 days or frozen up to 1 month (thaw in refrigerator). · Cookies keep in an airtight container at room temperature 4 days. If desired, palmiers can be recrisped in a 300°F oven until heated through, about 5 minutes.