In a stainless steel bowl, placed over a saucepan of simmering water, whisk together the egg whites, sugar, and salt. When this mixture is warm to the touch, and nice and creamy, remove from heat and stir in the vanilla extract, flour, and coconut. Cover and refrigerate for about two hours, or until firm.
Preheat oven to 325 degrees and line two baking sheets with parchment paper.
Place small mounds (heaping tablespoons) of the batter on the parchment-lined baking sheet, spacing several inches apart.
Bake for about 15 to 20 minutes or until golden brown. Remove from oven and let cool on the baking sheet for about 10 minutes and then place on a wire rack to cool.