Chocolate-gilded danish sugar cones

1/2 c  butter or margarine,
           -softened
    1/2 c  Sugar
    1/2 c  All-purpose flour
      2    Egg whites
      1 t  vanilla
      3 oz Bittersweet chocolate
           -OR
    1/2 c  Semisweet chocolate chips
 
  Preheat oven to 400'F. Generously grease 4 cookie sheets. Beat butter and
  sugar in large bowl until light and fluffy. Blend in flour. In clean, dry
  bowl, beat egg whites until frothy. Blend into butter mixture with
  vanilla.
  
  Using measuring teaspoon, place 4 mounds of dough, 4" apart, on each
  prepared cookie sheet. Spread mounds with back of spoon dipped in water to
  3" diameter. Bake, 1 sheet at a time, 5-6 minutes or until edges are just
  barely golden. (Do not overbake or cookies become crisp too quickly and
  are difficult to shape.) Remove from oven and quickly loosen each cookie
  from cookie sheet with thin spatula. Shape each into a cone; cones become
  firm as they cool. (If cookies become too firm to shape, return to oven
  for a few seconds to soften.)
  
  Melt chocolate in small bowl over hot, not boiling, water. Stir until
  smooth. When all cookies are baked and cooled, dip flared ends into melted
  chocolate. Let stand until chocolate is set. If desired, serve cones by
  standing them in a bowl. (Adding about 1" of sugar to bottom of bowl may
  be necessary to hold them upright.)
  
  Makes 16 cookies