Preheat oven to 400°F. Grease 4 cookie sheets.
Cream 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 a teaspoon, place 4 mounds of dough 4 inches apart on each prepared cookie sheet. Spread with small spatula dipped in water to 3 inches diameter. Bake 1 sheet at a time for 5 or 6 minutes or until edges are just barely golden. (Do not over bake or cookies become crisp too quickly and are difficult to shape.)
Remove from oven and quickly loosen each cookie from cookie sheet with a 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 water. Stir until smooth. When all cookies are baked and cooled, dip flared ends into melted chocolate; let stand until chocolate is set.
These are delicious with or without cream filling. ENJOY!