In a large bowl, beat egg yolks with sugar, salt, and vanilla until creamy. Fold egg whites into yolks using a wire whisk. Sift flour and anise into the bowl, and gently stir together with the whisk. Mix will look lumpy.
Put dough into decorating bag with round large tip, and press 1 inch rounds onto sheet. Let cookies sit out overnight at room temperature to dry.
The next day, cover cookies with a sheet of parchment paper, and bake at 350 degrees F (175 degrees C) for 20 to 25 minutes. Cookies are done when bottom is light brown, but tops are still almost white. Cool.
Store in container for 2 to 3 weeks in a cool place to mellow and to turn soft. You can add a slice of bread or a piece of apple to help soften the cookies.