Beat butter in a large bowl with electric mixer at medium speed until smooth.
Add powdered sugar; beat until well blended.
Add egg and vanilla; beat until well blended.
Combine candied fruit and walnuts in medium bowl.
Stir ¼ cup flour into fruit mixture.
Add remaining 2 ¼ cups flour to butter mixture; beat at low speed until blended.
Stir in fruit mixture with spoon.
Shape dough into 2 logs, each about 2” in diameter and 5 ½” long.
Spread coconut evenly on sheet of waxed paper.
Roll logs in coconut, coating evenly.
Wrap each log in plastic wrap.
Refrigerate 2-3 hours or overnight, or freeze up to 1 month. (Let frozen logs stand at room temperature about 10 minutes before slicing and baking).
Preheat oven to 350ºF.
Grease cookie sheets.
Cut logs into ¼” thick slices; place 1” apart on cookie sheets.
Bake 13-15 minutes or until edges are golden brown.
Transfer to wire racks to cool