1. In a large bowl beat butter with a mixer on medium 30 seconds. Add powdered sugar, lime zest, tequila, and vanilla. Beat until combined, scraping bowl as needed. Beat in flour, cornstarch, and salt.

2. Divide dough in half. Shape each portion into a 10-inch roll. Coat each roll with coarse sugar. If desired, sprinkle rolls with additional lime zest. Wrap rolls in plastic wrap or waxed paper. Chill 3 hours or until firm enough to slice.

3. Preheat oven to 325°F. Line cookie sheets with parchment paper. Using a sharp, thin-bladed knife, cut rolls into 1/4-inch slices. Place 2 inches apart on prepared cookie sheets. Bake 12 to 15 minutes or just until bottoms are golden. Transfer cookies on parchment to wire racks to cool. Drizzle cooled cookies with Tequila Icing. If desired, sprinkle with additional lime zest.

Tequila Icing

In a medium bowl combine 1 cup powdered sugar, 1 Tbsp. tequila, and 1 Tbsp. milk. Whisk until smooth, adding more milk, 1 tsp. at a time, to reach spreading consistency.