In the bowl of an electric mixer beat the butter, sugar, lime zest, extract and eggs on medium-low speed until well combined. Add flour and salt; beat until soft, non-sticky dough forms. You should be able to handle the dough without it sticking to your fingers. If dough is sticky, beat in additional until the dough comes to the correct consistency.
Shape dough into a ball and remove 1/3. Roll into a ball and cover with plastic wrap. Chill for 15 minutes. Return 2/3 dough to the mixing bowl and add green food color. Remove dough from bowl. Divide green dough in half and roll each portion to 6-inch batons. Chill until firm, about 30 minutes.
On lightly floured work surface, roll plain dough into a rectangle. Place a roll of green dough on the plain dough. Roll plain dough in a single layer around green dough. Cut away excess dough; reserve scraps for second green dough portion. Repeat process with remaining green dough and remaining plain dough.
Place green sanding sugar on plate; roll dough batons in sugar until completely coated. Wrap sugar-coated dough logs in plastic wrap and freeze until semi-solid (they’ll slice easier!).
Preheat oven to 400°F. Line cookie sheets with parchment paper.
Cut chilled dough into 1/4-inch-thick rounds. With the back edge of a butter knife, score “segment” lines into each round, making only indentations (do not go all the way through). Leave whole for “lime wheels” or cut rounds in half; place on cookie sheets.
Bake 6 to 8 minutes or until set. Remove cookies from cookie sheets to cooling racks. Cool completely.