In the bowl of an electric mixer fitted with the paddle attachment, cream butter and sugar until light and fluffy, 3 to 4 minutes. Add egg; beat until just blended. Add citrus zests, lime juice, and almond extract.

With the mixer on low speed, add flour and cornmeal. Continue beating until well blended. Transfer dough to a piece of plastic wrap. Shape the dough into a disk, wrap, and chill until firm, about 1 hour.

Preheat oven to 350 degrees. Line two baking sheets with Silpats or parchment paper. Fill a small bowl with cornmeal. Using a 1 1/4-inch ice-cream scoop, form balls from chilled dough. Place balls on prepared sheets, spaced about 3 inches apart. Dip bottom of a medium drinking glass into cornmeal. Flatten balls with the bottom of glass until dough is about 1/4 inch thick.

Bake cookies until crisp and light-golden brown around the edges, 14 to 16 minutes. Transfer baking sheets to a wire rack, and let the cookies cool completely.

Place a wire rack on top of a piece of parchment paper. Pour the lime glaze over the cooled cookies, allowing the excess to drip off the edges. Let glaze set. Store cookies in an airtight container for up to 1 week.

LIME GLAZE

Makes 1 1/3 cups

3 1/4 cups confectioners sugar

8 tablespoons fresh lime juice, plus 2 1/2 teaspoons freshly grated lime zest (about 6 limes total)

Directions

Sift confectioners' sugar into a medium bowl. Add lime juice; stir until smooth. Stir in lime zest. Use glaze immediately.