In a large bowl, using an electric mixer, beat butter at medium speed until smooth. Add confectioners’ sugar; beat until blended. Add egg and vanilla; beat until well combined.
In a separate bowl, combine candied fruit and nuts. Stir ¼ cup flour into fruit mixture. Add 2 ¼ cups flour to the butter mixture; beat on low speed until well blended. Stir in fruit mixture with a wood spoon.
Shape dough into 2 logs, each about 2-inches in diameter and 5 1/2 –inches long. Spread coconut evenly on a baking sheet. Roll logs in coconut, coating evenly. Wrap each log in plastic wrap. Refrigerate 2-3 hours or overnight.
Let logs stand at room temperature for about 10 minutes before slicing and baking.
Preheat oven to 350 degrees. Line cookie sheets with parchment paper.
Cut logs into ¼-inch slices; place 1-inch apart on prepared cookie sheets.
Bake 13-15 minutes or until edges are golden brown. Transfer to wire racks to cool. Store cooled cookies in an airtight container.