Preheat the oven to 350° F. Line two baking sheets with parchment paper and set aside.
Separate the eggs whites and yolks into two bowls. Whisk together the yolks, along with ¼ cup (50 g) granulated sugar and vanilla extract, until smooth, thick, and a little lighter in color.
Using the whisk attachment, whip the egg whites until frothy and soft peaks form. Slowly add ¼ cup (50 g) granulated sugar while whipping constantly. Continue to whip until stiff peaks form.
Gently fold a large spoonful of the egg whites into the egg yolk mixture to loosen it slightly. Then fold the rest of the egg whites into the mixture carefully.
Put a sieve over the bowl and sift the flour and salt into the eggs. Gently fold the flour in until no more lumps of flour are visible.
Fill a large pastry bag fitted with a ½-inch round tip (or a gallon ziptop bag with one corner cut off) and pipe 3½-4 inch long fingers onto 2-3 parchment-lined baking sheets.
Mix together the final ¼ cup sugar plus the powdered sugar and sift over the cookies. Some of the mixture will get in between the cookies on the baking sheet, which is fine.
Bake one sheet at a time for 14-15 minutes, or until slightly risen, somewhat cracked and firm to the touch. Cool on baking sheet for 5 minutes, and then transfer to a cooling rack to cool completely. Cookies are slightly soft when first baked, but become crispy as they sit. To use in a recipe, leave them set at room temperature overnight or up to a few days.