1. Combine flour and cornmeal. Beat butter and sugar at medium speed with an electric mixer until light and fluffy. Add egg and next 3 ingredients, beating until blended. Gradually add flour mixture, beating just until blended after each addition. Cover and chill dough 1 hour.
2. Shape dough into a 12-inch log using wax paper. Wrap tightly in plastic wrap, and chill 8 hours.
3. Preheat oven to 375°. Cut log into 1/4-inch-thick slices. Place 1 inch apart on ungreased baking sheets. Bake 12 minutes or until set. Transfer to wire racks; cool completely (about 15 minutes).
Try This Twist!
Chocolate-Orange Cornmeal Cookies: Substitute orange zest and fresh orange juice for lime zest and juice. Drizzle 1/4 cup melted semisweet chocolate morsels over cooled cookies.