Add the egg whites and vanilla extract to a medium bowl and use a whisk or hand mixer to beat until frothy, about 1 minute.
Sift in the flour, sugar, and salt through a fine-mesh sieve.
Using a spatula, gently incorporate into the batter until paste-like.
Add the water, 1 tablespoon at a time, until the batter is smooth and falls into ribbons when the spatula is picked up.
Place 1 tablespoon of batter onto a silpat-lined baking sheet and spread into a 3-inch (7-cm) circle.
Repeat with another tablespoon of batter, making sure to only leave two circles on the silpat.
Bake for 8 minutes, until the edges become golden brown.
Working quickly, use a spatula to remove the cookies from the pan. Add a fortune in the middle, fold the cookies in half, then place the flat side on the lip of a cup, folding the edges down into a fortune cookie shape. Place the folded fortune cookies in a mini muffin tin until cooled to retain their shape.