Line a baking sheet with waxed paper; set aside. In a large saucepan, cook butter over medium-low heat until golden brown, about 5 minutes. Remove from the heat; stir in the coconut, sugar and cream.
Drop by rounded teaspoonfuls onto prepared baking sheet. Refrigerate until easy to handle, about 25 minutes.
Roll mixture into balls, then shape each into a cone. Return to baking sheet; refrigerate for 15 minutes.
Meanwhile, in a microwave, melt chocolate chips and shortening; stir until smooth. Dip bottoms of cones into chocolate; allow excess to drip off. Return to waxed paper to harden. Store in an airtight container in the refrigerator. Yield: about 3 dozen.