1. Preheat the oven to 325°F with a rack set in the lower center position. Line two baking sheets with silicone baking mats or buttered parchment paper.

2. Whip the egg whites in a large, clean, dry bowl until they are foamy, then gradually add the sugar, continuing to beat until they just begin to hold a stiff peak but are not at all dry. Beat the yolks in a separate bowl with the vanilla until they are light and pale. Gently fold the yolks into the whites until they are almost combined but still streaky. Sift in the flour, gently folding it in until it is just combined.

3. Transfer about half of the mixture to a pastry bag fitted with a standard round tip, or to a resealable plastic bag. If using the plastic bag, force the mixture into one corner, twist the bag at the corner to close it off, then snip off the corner to form about a ¾-inch round opening. Pipe the batter onto the prepared baking sheets in 3-inch-long fingers, continuing with the remaining batter, to form 36 cookies.

4. Bake until the cookies just barely begin to color, about 15 minutes. Transfer the pan to a rack to cool until the cookies can easily be peeled from the mat or paper.