Preheat oven to 350°F (180°C). Line a baking tray with parchment paper. Set aside.
Add egg whites and sugar to a large bowl. Whip on high speed for 2 minutes until the eggs are frothy.
Add butter, vanilla, water, and salt, and mix until combined.
Add flour and mix until combined. Divide batter into one bowl for each colour you are using.
Add food colouring to each bowl, a bit at a time, until you get the shade you prefer.
Place each batter colour into piping bags and cut off about 3mm at the ends. Alternatively you can place the batter in ziplock bags and cut the corner off.
Pipe 3-inch circle outlines with one of the batter colours. I have a template to use as a guide in the notes below.
Pipe the rainbow stripes within the circle, alternating colours. Repeat with another 1-2 cookies. I don't recommend baking more than 3 cookies at a time, as you need to be quick in forming them when they come out of the oven.
Bake for 7-8 minutes or until the edges are slightly golden. If you undercook, the cookies will be too soft to form. If you overcook, they will be too hard to form.
Quickly remove cookies from the oven. Flip one over, and fold it in half, pinching only the top closed. Don't pinch the sides. Insert a fortune then place cookie on the rim of a cup to shape it into a fortune cookie. Repeat with the remaining cookies.
Store cookies in an airtight container at room temperature for 3 days.