In a large bowl, beat butter, confectioners sugar, milk and vanilla until blended. Stir in coconut and pecans. Divide dough in half; refrigerate, covered, 1 hour.

Working with half the dough at a time, shape mixture into 1-in. balls; place on waxed paper-lined baking sheets. Refrigerate 30 minutes longer.

In top of a double boiler or a metal bowl over barely simmering water, melt chocolate chips and shortening; stir until smooth. Dip balls in melted chocolate; allow excess to drip off. Return to waxed paper. Top with additional coconut if desired. Refrigerate until set.

To Make Ahead: Store in an airtight container in the refrigerator.