Preheat oven to 400° F.
Whip your egg whites until stiff peaks form.
Add the flour and sugar to your egg whites. Combine.
Stir in the water, vanilla extract, and food coloring.
Line a baking sheet with parchment paper or a silpat.
Spoon 1 tablespoon of batter onto the baking sheet and use the back of a spoon to form a circle. I recommend only doing 2-3 cookies on a baking sheet so that you have time to fold each one before they start to cool and dry.
Bake for 3-5 minutes or until the edges are light golden brown. I found that my first batch was able to go for the full 5 minutes, but as the oven and baking sheet got hotter over time, the next batches would cook in about 3 minutes.
Take the baking sheet out of the oven and use a metal spatula to carefully lift the cookie off of the sheet. Place your fortune onto the circle, fold the circle in half, and then place the bottom of the half-circle over the rim of a glass so that it forms into a fortune cookie. I'll link a video below!
Let it cool in a muffin tin or something else that will help it keep it's circle form.