Preheat oven to 350F. Line a baking sheet with a baking mat or parchment paper.
In a mixing bowl, beat butter and sugar until light and fluffy, 2-3 minutes. Add vanilla and egg whites and mix until incorporated.
Reduce mixer speed to low and add in flour just until incorporated.
Remove 1-2 tablespoons of batter to a small bowl and add food coloring.
Put 1 tablespoon of plain batter on the baking mat and spread into a 4-6" oval. You want it very thin!
With a toothpick drag some of the colored batter across the cookie to make stripes (I used a knife to make two wider stripes instead of 5-6 skinny stripes).
Bake at 350F for about 7 minutes, until the edges just begin to turn golden brown. Watch carefully! If the cookies are overbaked they will not roll.
Remove from the oven and let sit for about 30-45 seconds. Remove a cookie from the pan and roll around a chopstick, wooden spoon handle, etc. to make a thin tube. You need to work quickly before the cookies harden.