Combine the softened butter and granulated sugar in a mixing bowl. Use a hand or stand mixer to beat until the mixture is light and fluffy, with a pale color and slightly increased volume, about 2-3 minutes.
Add the lightly beaten egg and lime zest to the creamed mixture. Mix on low speed until fully incorporated, and you see a cohesive, slightly glossy batter with a uniform texture.
In a separate bowl, whisk together the all-purpose flour, baking powder, salt, and additional lime zest if desired. Gradually add this dry mixture to the wet ingredients, mixing on low speed to form a soft dough that begins to come together.
Transfer the dough onto a lightly floured surface. Knead gently until smooth, about 30 seconds. Shape the dough into two equal disks, wrap in plastic wrap, and refrigerate for at least 30 minutes to firm up.
Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper. Remove one dough disk from the refrigerator and roll it out to about 1/4 inch thickness. Use cookie cutters to cut out shapes and place them on the prepared baking sheet.
Bake the cookies in the preheated oven for 8-10 minutes, or until the edges are lightly golden and the surfaces shimmer slightly. Remove from oven and allow to cool on the baking sheet for 2 minutes before transferring to a wire rack to cool completely.
