Step 1

Preheat oven to 350°F. Line a baking sheet pan with parchment paper.

Step 2

Add sugar and lime zest to a small bowl. Use a fork or your fingers to rub the zest into the sugar for 1-2 minutes. The goal is to extract as much lime zest and infuse the flavor into the sugar.

Step 3

With an electric mixer, beat the butter and lime-sugar on high until light and fluffy, 3-4 minutes. Add the eggs one at a time, mixing after each, then the vanilla extract.

Step 4

In a separate bowl, combine the flour, cornmeal, baking powder, and salt. Add to the wet ingredients and mix until just combined.

Step 5

Place rounded tablespoons of dough (I used a #40 1½ Tbsp cookie scoop) on the prepared sheet pan about 2 inches apart. Gently press each ball with the palm of your hand to flatten slightly.

Step 6

Bake until the edges are just turning golden brown and centers are still pale, about 17-20 minutes. Do not over-bake. Let cool on the sheet pan for 5 minutes, then remove to a cooling rack to cool completely.

Step 7

To make the glaze, whisk together the powdered sugar, lime zest, and lime juice. Add milk 1 teaspoon at a time if needed to reach the consistency you want. It should be thin enough to spread over the cookies.

Step 8

Glaze the cookies on a wire rack with a sheet pan placed underneath to catch excess glaze. Let the glaze harden for several minutes before serving.

Step 9

These cookies are best served the day they are made, but will keep in an airtight container at room temperature for a few days.