Preheat the oven to 350°F. Line a baking sheet with parchment paper.
In a bowl, add and whip the egg whites until frothy with a whisk or electric hand mixer, then add the sugar.
Continue to whip the egg whites until they reach a firm peak. To tell if the egg whites are at a firm peak: dip your whisk into the egg whites and pull it straight out. Flip the whisk upside down, and the tip will fold over onto itself. If the egg whites are soft and not holding their shape at all, keep whisking.
Whisk in the vanilla extract and almond extract.
Gently fold in the shredded coconut.
Use a small cookie dough scoop or spoon to form the cookies onto your baking sheet. This will make 12-16 cookies depending on the size of your scoop.
Bake for 18-22 minutes, until the outside of the cookie is a light golden brown.
Store in an air tight container up to 5 days.