These key lime cookies have a sweet, tart citrusy flavor with a satisfying crunch from the sparkling sugar rim and sweet glaze to finish them. Citric acid amplifies the tartness in these cookies, but you can make them with just lime juice and zest for a more subtle flavor.
In a medium bowl, combine the flour, powdered sugar, salt, cornstarch and citric acid. Set aside.
In a large bowl, use a hand mixer to beat the softened butter, lime zest and lime juice until creamy. Add about half of the flour mixture and mix in until just combined. Add the rest of the flour, and mix until it forms a soft dough.
Cut two large pieces of plastic wrap and lay them flat on a work surface. Divide the dough in half. Place one half in the center of one piece of plastic wrap. Fold the plastic wrap over on the dough and work the dough into a 10" log. Repeat with the second piece of dough.
Sprinkle the cookie dough log with colored sugar and roll it back and forth on the parchment paper until the log is evenly coated with colored sugar. Wrap tightly and refrigerate for at least 2 hours and up to 5 days.
Remove the dough and make sure that the log is round, by rolling it on a flat surface. If you have one or more areas of the dough that have flattened out from resting, roll them a little more until they're round and refrigerate for an additional 10-20 minutes, until firm.
Preheat the oven to 350 degrees. Line two baking sheets with parchment paper or a silpat and set aside.
Use a very thin, sharp knife to slice the cookies into 1/4" slices. Place 1" apart on the cookie sheets and bake 9-11 minutes until edges are lightly browned. Cool for one minute on the cookie sheet, then transfer to a wire rack to cool completely.
To make the glaze
Mix the powdered sugar and cream together until smooth. The icing should be soft and spreadable, but thicker than drizzling consistency.
To glaze the cookies
After the cookies have cooled, spoon a little of the glaze on top and smooth out with the back of a spoon. Sprinkle with the sparkling sugar and let stand until the glaze has hardened.
To store the cookies: keep them in an airtight container at room temperature. Separate stacks of cookies with parchment paper to prevent sticking.