Let the butter come to room temperature or microwave for 20-30 seconds to soften. Add half of the sugar and mix until creamy.
Beat egg whites. While beating the egg whites, add remaining sugar in 3 batches. Continue beating until stiff peaks form and the meringue is ready.
Add 1/3 of the meringue from Step 2 to the butter and sugar from step (1). Mix well.
Sift the cake flour and add it to the bowl. Mix well.
Add the mixture from Step 4 to the remaining meringue and mix until it's no longer floury.
The dough is finished Spoon the dough into a piping bag or plastic bag and cut a 1 cm hole in the tip of the bag (if it's too much of a bother, you could spoon the batter onto the baking sheet).
Pipe the batter into 6 cm ovals. They will melt and expand while baking, so leave some space between the cookies so they're not too close together. If you want circular cookies instead of ovals, they'll look cute too.
Bake in a preheated oven at 170ºC for about 13-17 minutes, checking the cookies every so often. They should be golden brown around the edges when done.
Let the cookies cool and they're done. They will be soft right after baking, but will harden as they cool. You could spread them with chocolate or other fillings to make sandwich cookies.
For Step 6, the dough will be really soft, so it may be hard to get it into the piping bag or plastic bag. Setting the bag in a cup will help you.
Story Behind this Recipe
I wanted to consume leftover egg whites, so I decided to make langue de chat. I used round numbers for the ingredient amounts. You'll find yourself reaching for more and more of these light, crispy cookies.
The key is to whip the meringue well until stiff peaks form! Bake until the edges are golden brown. If the cookies are underbaked, they will be very light and fluffy (some may prefer a more cakey texture though.)