Bake 8 minutes for a soft and chewy cookie or up to 12 minutes for a crisp cookie.
Beat first 4 ingredients at medium speed with an electric mixer until fluffy. Add eggs, 1 at a time, beating just until blended after each addition.
Stir together flour and next 2 ingredients; gradually add to butter mixture, beating just until blended after each addition. Stir in coconut, chopped macadamia nuts, and lime zest.
Shape dough into 4 logs (about 2 inches in diameter); wrap each log in plastic wrap. Chill 8 hours to 3 days.
Preheat oven to 350°. Cut each log into 1/4-inch-thick slices; place on parchment paper-lined baking sheets. Bake 8 to 12 minutes or until lightly browned. Remove from baking sheets to wire racks, and cool completely (about 20 minutes).