Preheat the oven to 325 degrees F and line a baking sheet with parchment paper. Whisk the egg whites, sugar, cocoa powder, cinnamon, orange zest, salt and vanilla in a large bowl until combined; fold in the coconut.
Scoop heaping tablespoonfuls of the coconut mixture about 1 inch apart onto the baking sheet. Use your fingers to form into pyramids. Bake until golden brown around the edges, 20 to 25 minutes. Let cool 10 minutes on the baking sheet, then transfer to a rack to cool completely.