Position two racks near the middle of the oven and preheat to 275F. Line two large baking sheets with parchment paper or silicone baking mats. Set aside.

In the bowl of a stand mixer with the whisk attachment or in a large bowl with a hand mixer, beat the egg whites on high until very stiff. They should be stiff enough that when you glide the tip of a sharp knife through it the egg white pulls apart from itself. Add the sugar and vanilla extract and beat again on high until the sugar is dissolved and the mixture is glossy. To check if the sugar is dissolved, rub a small amount of it between your fingers. If you can still feel the sugar granules, keep beating on high until the mixture feels smooth between your fingers.

Sieve the cocoa powder onto the egg white mixture to ensure there are no lumps, add the coconut, then gently fold together using a spatula.

Drop heaping tablespoons onto the baking sheets about 1 1/2 inches apart. Bake both trays at the same time for 25 minutes or until the bottoms are just barely golden and the tops are firm. Cool to room temperature on the baking sheets before removing cookies.