1. Beat butter at medium speed with an electric mixer until creamy. Gradually add sugar, beating until smooth. Stir in 1 Tbsp. Key lime zest and juice until blended.
2. Stir together flour and next 2 ingredients. Gradually add flour mixture to butter mixture, beating at low speed until blended.
3. Divide dough in half; flatten each into a disk. Roll each disk to 1/4-inch thickness between 2 sheets of wax paper. Transfer dough, in wax paper, to a baking sheet; chill 1 hour.
4. Preheat oven to 350°. Working with 1 portion of dough at a time, remove top wax paper; cut with a 2-inch star-shaped cutter, rerolling dough scraps once. Place 1 inch apart on parchment paper-lined baking sheets. Stir together white sanding sugar and 1 Tbsp. lime zest. Sprinkle cookies with sugar mixture, pressing gently to adhere.
5. Bake at 350° for 14 to 16 minutes or until tips of stars just begin to brown. Cool on baking sheets 1 minute; transfer to wire racks. Cool completely. Store in airtight containers.