1Beat butter and sugar together with an electric mixer on medium-high speed. Beat in the egg whites, one at a time. Beat in the vanilla.
2Lower the speed and add the flour or flour-cocoa mixture (see Cook's Note) and mix until just combined. Do not overmix. Cover bowl and chill for at least 1 hour.
3Preheat oven to 325 degrees F (165 degrees C).
4Cut a small hole (about 3 1/2 inch diameter) in a thin piece of cardboard or plastic to serve as a template in forming the tuiles. Line a cookie sheet with parchment paper or a silicon mat and place the stencil on it. Using a small off-set spatula, place a small amount of the batter in the center of the hole of the stencil and spread it out evenly. Carefully lift the stencil off. Repeat for more cookies.
5Bake in preheated oven until lightly brown around the edges, 8 to 10 minutes. Remove from the oven and while still hot, remove tuiles from the pan and drape them over a rolling pin. Allow to sit a few minutes to harden and cool. Store in an airtight container.
To create Chocolate Tuiles, substitute 3/4 cake flour sifted with 5 tablespoons Dutch-processed cocoa powder for the 1 cup cake flour.
The plastic lids from yogurt or cottage cheese containers are perfect for making stencils.
Shape the tuiles however you like: drape the hot cookies over a rolling pin, over a glass, or in the hollows of an empty egg carton.