Heat the oven to 400° F (350° F if you're using a dark-coated baking sheet). In a medium-size bowl, beat the sugar and egg whites with an electric mixer for 30 seconds.
Mix in the flour until smooth, then add the vanilla extract and melted butter. For each cone, scoop 2 1/2 tablespoons of batter onto the baking sheet, spreading the batter into thin 6-inch circles (use a measuring spoon for accuracy).
Bake for 7 or 8 minutes or until golden, then remove the sheet from the oven. Working quickly, form each cookie into a cone (a parent's job), pinching the tip to seal it tightly. Allow the cones to cool seam side down on a rack.
Tip: If a cookie begins to cool and is difficult to shape, return it to the oven briefly to soften it.
No-drip Tip: The next time you serve ice cream in cones, place a mini marshmallow in the tip of each cone before scooping on the ice cream. The added treats will help prevent melted ice cream from leaking out the bottoms of the cones.