Peppermint is a holiday baking mainstay, but you love it or hate it. I’ve drafted lime zest to help win over the peppermint-averse; the combination works because the bitter, floral quality of the zest tames the peppermint’s potentially cloying sweetness. I use only crushed soft peppermint candies, not extract, to keep the flavor present but not overpowering (their soft texture also makes slicing the cookie dough a breeze). The sparkling sugar painted on the outside of the cookie logs adds to their über-crispiness. I use red to highlight the color of peppermints, but you can also use green for the lime, a mix of both colors, or simple turbinado sugar, which has the same coarse texture and is easy to find in grocery stores (look for Sugar in the Raw brand).
In a large bowl, combine the butter, sugar, lime zest, vanilla and salt and beat with an electric mixer on low speed until smooth, about 1 minute (see Baker’s Note). Mix in the peppermints, then add the flour and mix on low speed until just combined.
Split the dough in half and place each half on a sheet of parchment paper, forming each into a rough log lengthwise down the center of the paper. Fold one long edge of the paper over the log to cover it, then use a ruler or bench scraper to press the paper against the dough to tighten it into an even log, roughly 12 inches long. Wrap the log up completely in the paper and twist the ends like candy wrappers to close. Repeat with the other dough log, then refrigerate both logs until firm, at least 30 minutes.
Unwrap 1 dough log and brush it all over lightly with some beaten egg white. Sprinkle the log with ½ cup red sparkling sugar until completely coated. Transfer the log to a sheet of plastic wrap and wrap up completely. Return to the refrigerator to allow the egg white and sugar to set, at least 30 minutes or up to overnight. Repeat with the second dough log, more egg white and the remaining ½ cup sparkling sugar.
Heat the oven to 350 degrees. Line 2 baking sheets with parchment paper.
Unwrap 1 log and cut into ¾-inch-thick disks, rotating the log a quarter turn after each slice to keep each disk round (you should get at least 15 cookies, minus the trimmed ends). Arrange the disks evenly on one of the prepared baking sheets. Repeat with the second log and second baking sheet.
Bake, rotating the baking sheets from front to back and top to bottom halfway through, until cookies are set and the edges are very lightly browned, about 18 minutes.
Let the cookies cool on the baking sheets for 1 minute before transferring to a wire rack to cool completely.
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