Preheat oven to 350 degrees F (175 degrees C). Grease a large cookie sheet.
In a large bowl, beat egg whites, confectioner's sugar, and flour until blended and smooth. Beat in melted butter, anise extract, and salt.
Drop 1 heaping teaspoon mixture onto cookie sheet. Repeat to make 3 more cookies, about 3 inches apart. With small spatula, spread cookie to a 3-inch round. (Do not place more than 4 on cookie sheet because, after baking, cookies must be shaped quickly before hardening.).
Bake cookies 5 to 7 minutes until edges are golden. With pancake turner, quickly remove 1 cookie to wire rack. With hands, gently shape warm cookie to flute edges. Repeat with remaining cookies on cookie sheet. If cookies become too hard to shape, return cookie sheet to oven to soften cookies slightly. Repeat with remaining batter. (Batter will become slightly thicker upon standing.) Store in tightly covered container.