Preheat your oven to 350°F (175°C) and line a cookie sheet with parchment paper.
In a mixing bowl, cream together the softened butter and granulated sugar using a hand or stand mixer until the mixture is light, fluffy, and pale in color—about 2-3 minutes. You should hear a gentle whirling and see the color brighten.
Add the lime zest and vanilla extract to the butter mixture and mix until evenly incorporated, releasing fragrant citrus aromas.
Gradually add the flour to the wet ingredients, mixing on low speed until just combined and the dough begins to come together.
Pour some coarse sugar onto a small plate. Scoop roughly one tablespoon of dough and roll it into a ball, then press it slightly to form a thick disc.
Roll each dough piece in the coarse sugar until fully coated, creating a sparkly, textured surface.
Place the coated dough balls onto the prepared baking sheet, spacing them about 2 inches apart to allow for spreading.
Bake in the preheated oven for 8-10 minutes, or until the edges are just golden and the centers look set but still soft.
Remove the cookies from the oven and let them cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely and set their texture.
Once cooled, enjoy these fragrant, tangy cookies with their crisp exterior and tender interior, perfect for a bright citrus treat.
