Preheat the oven to 400F. Place the butter in a mixing bowl and beat it with a wooden spoon or hand-held mixer until creamy. Sift the sugar over the butter and beat it in. Add the egg whites, one at a time, beating well after each addition. Stir in the vanilla extract and the flour, and mix well. Fit a large pastry bag with a 5/16-inch plain pastry tube. Scoop the batter into the pastry bag, and pipe the batter into fingers 2 1/2 inches long and 1/2 inch wide, arranging them on greased cookie sheets in staggered rows and separating them by 1 1/2 inches. The ends of each finger should be fatter than the center, like a dumbbelll. Bake 8-10 minutes, until lightly browned around the edges but still pale in the center. Slide the cookies onto a wire rack and let cool to room temperature.
