Preheat oven to 425 F (220 C). Grease several baking sheets with butter. In a medium-size bowl beat 1/4 cup butter with powdered sugar until creamy; beat in vanilla. Gradually beat in egg whites. Fold in flour, then 2 tablespoons melted (cooled) butter. Drop small teaspoonfuls of mixture onto prepared baking sheets, spacing well apart; flatten each teaspoonful slightly. Bake about 8 minutes or until lightly browned around edges. Using a spatula, immediately remove cookies from baking sheet to a wire rack; cool. Melt chocolate in a small bowl placed over a pan of hot, but not boiling water. When cookies are cool, spread each one with a thin layer of melted chocolate; allow chocolate to set slightly then sprinkle with coconut. Place in a cool place until chocolate sets completely.