I made this for a get together...and they were a big hit.
Here's the original link from SmittenKitchen
Here's the recipe (I made half a batch).
12 tablespoons (1 1/2 sticks) unsalted butter, room temperature
1 cup confectioners’ sugar
Grated zest of 4 tiny or 2 large key limes
2 tablespoons freshly squeezed lime juice
1 tablespoon pure vanilla extract
1 3/4 cup plus 2 Tablespoons all-purpose flour (a.k.a. 2 cups minus 2 tablespoons)
2 tablespoons cornstarch
1/4 teaspoon salt
1. In the bowl of an electric mixer fitted with the whisk attachment, cream butter and 1/3 cup sugar until fluffy. Add lime zest, juice, and vanilla; beat until fluffy.
2. In a medium bowl, whisk together flour, cornstarch, and salt. Add to butter mixture, and beat on low speed until combined.
3. Between two 8-by-12-inch pieces of parchment paper, roll dough into two 1 1/4-inch-diameter logs. Chill at least 1 hour.
4. Heat oven to 350 degrees. Line two baking sheets with parchment. Place remaining 2/3 cup sugar in a resealable plastic bag. Remove parchment from logs; slice dough into 1/4-inch-thick rounds. Place rounds on baking sheets, spaced 1 inch apart.
5. Bake cookies until barely golden, about 15 minutes. Transfer cookies to a wire rack to cool slightly, just three or four minutes. While still warm, place cookies in the sugar-filled bag; toss to coat. Bake or freeze remaining dough. Store baked cookies in an airtight container for up to 2 weeks.