Heat a shallow skillet over medium heat and toast the pine nuts until the surface oils are fragrant and golden, about 3 to 4 minutes.

In a food processor, pulse the granulated sugar, coconut flakes, lime zest, and fresh thyme to achieve a fine, botanical-infused sugar base.

In a separate bowl, whisk together the flour, cornmeal, baking powder, and salt to ensure uniform distribution.

Using an electric mixer, cream the butter with the infused sugar base until light and aerated.

Incorporate the eggs, vanilla, and 2 tablespoons of the lime juice. Gradually stir in the dry ingredient mixture followed by the toasted pine nuts.

Divide the dough into two equal portions, encapsulate in plastic wrap, and place in the freezer for 15 minutes to stabilize the fat.

Preheat the oven to 350°F. Line a heavy baking sheet with professional parchment paper.

Shape each dough portion into a uniform log approximately 3 inches wide and 10-12 inches long.

Bake for 20 minutes until the logs achieve initial integrity and a light golden hue. Remove from heat and allow to cool for at least 15 minutes.

Reduce the oven temperature to 300°F.

Utilizing a serrated knife, execute 1/2-inch transverse slices. Arrange the slices cut-side up on the baking sheet.

Return to the 300°F oven and bake for an additional 30 minutes until the cookies are thoroughly dried and crisp. Transfer to a rack to cool completely.

Whisk together the confectioner’s sugar, half-and-half, vanilla, and the remaining 1 tablespoon of lime juice until a smooth glaze is formed.

Drizzle the glaze over the cooled biscotti and allow to set before service.