1. In a deep bowl with mixer on high speed, whip egg whites to a thick foam. Continue to beat, adding 1 tablespoon of sugar about every 15 seconds until whites hold very stiff peaks, about 6 minutes total. Mix in vanilla.
2. Sprinkle cocoa over egg whites and fold in gently with a flexible spatula. Add coconut and pecans and fold into mixture (the volume decreases).
3. Drop mixture in 1-tablespoon portions about 1 inch apart on buttered 14- by 17-inch baking sheets.
4. Bake cookies in a 325° oven until firm and dry to touch, about 15 minutes. If baking more than 1 pan at a time, switch positions after 7 or 8 minutes.
5. Slide a wide spatula under cookies and transfer to racks to cool. Serve, or store airtight at room temperature up to 1 week.
Nutritional analysis per cookie.