Preheat oven to 350°. In a large bowl, cream butter and brown sugar until light and fluffy. Beat in egg and vanilla. Combine flour, baking powder, baking soda and salt; gradually add to creamed mixture and mix well. Stir in German sweet chocolate, coconut and pecans.
Roll into 3/4-in. balls. Place 2 in. apart on ungreased baking sheets. Bake 10-12 minutes or until edges are browned. Remove to wire racks to cool.
In a microwave, melt semisweet chocolate and shortening; stir until smooth. Dip tops of cookies into chocolate mixture; allow excess to drip off. Place on waxed paper-lined baking sheets; sprinkle with toasted coconut. Chill 1 hour or until firm.