Place coconut, pecans and dates together in a food processor, pulse until finely ground and combined, and set aside. Sift together flour, baking soda and spices, and set aside. Cream sugars and shortening together in a standing mixer until light and fluffy. Add eggs, buttermilk and anise extract, and mix until thoroughly combined. Stir in flour mixture until combined, and then fold in ground coconut, nuts and fruit mixture. Dough should be stiff. Allow dough to chill until ready to use.
Preheat oven to 350 degrees. Once dough has chilled, shape into 1-inch balls and place about 2 inches apart on a parchment-lined baking sheet. Bake for 8 to 10 min. Transfer cookies to wire rack to cool. Once cool, dip in powdered sugar to coat, shaking off any excess sugar. Store in an airtight container.