Preheat the oven to 350 degrees F. Line two 11-by-17-inch baking sheets with parchment paper.
Add the sugar and cinnamon to a small bowl. Stir with a fork until well blended, and set aside.
Lightly flour a counter or cutting board. Roll the dough out to 1/4-inch thick. Use a 1-inch cookie cutter to cut out the cookies (doughnut and biscuit cutters usually come with a small circle cutter in the center). Place the cookies on the prepared baking sheets. Sprinkle the cookies with some of the cinnamon-sugar mixture. Bake, one tray at a time, until golden around the edges, 12 to 14 minutes.
Dice the butter and return it to the refrigerator while you prepare the flour mixture. Place the flour, salt, and sugar in the bowl of a food processor fitted with a steel blade and pulse a few times to mix. Add the butter and shortening. Pulse 8 to 12 times, until the butter is the size of peas. With the machine running, pour the ice water down the feed tube and pulse the machine until the dough begins to form a ball. Dump out on a floured board and roll into a ball. Wrap in plastic wrap and refrigerate for 30 minutes.
Cut the dough in half. Roll each piece on a well-floured board into a circle, rolling from the center to the edge, turning and flouring the dough to make sure it doesn't stick to the board. Fold the dough in half, place in a pie pan, and unfold to fit the pan. Repeat with the top crust.
Make a fancier version of this cookie by shaping them into bowties. Cut the rolled out dough into 1 1/2-by-3-inch rectangles. Place the cutouts on a parchment-paper-lined baking sheet. Use your fingers to pinch the center of each rectangle, to form a bowtie shape. Bake until golden around the edges, 15 minutes.
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