Using a mixer, cream butter, sugar and vanilla on low speed until blended. Gradually add the egg whites. Add the flour in small batches and mix just until the batter is smooth. Be careful to not over-mix.
Cover the bowl with plastic wrap and chill in the fridge for at least 30 minutes to firm up. (This batter will keep in the fridge for up to a week, take it out 30 minutes before you plan to use it).
Preheat the oven to 350°F.
Line a baking sheet with parchment paper, Silpat, or grease with either butter or non-stick spray and chill the baking sheet in the fridge for at least 15 minutes. This will help the batter spread more easily if using a stencil/cardboard template. Press the stencil on the baking sheet and use an offset spatula to spread batter.
Bake for about 5-10 minutes or until the edges turn golden brown. Remove from oven.
Cut the rectangular cookie into strips using a sharp pizza cutter or knife. (If using a knife cut straight downward, do not use a sawing motion.)
To shape corkscrews, wrap one strip in a spiral around the handle of a wooden spoon and place it on a wire rack to cool completely before removing the wooden spoon, about 2 minutes. Repeat with remaining strips on additional handles if possible.
These cookies have to be shaped when still warm, you might want to bake a small amount at a time or put them in the oven to warm them up again. Or: place a baking sheet toward the front of the warm oven, leaving the door half open. The warmth will keep the cookies malleable.