Prepare the Mixture: Preheat the oven to 190°C (375°F). In a large bowl, mix the shredded coconut and sugar together. Add the egg whites and mix vigorously until the mixture is smooth and slightly sticky, ensuring the sugar begins to dissolve and bind the coconut.
Shape the Cookies: Transfer the coconut mixture to a large piping bag fitted with a star-shaped nozzle to create textured ridges. Pipe out small individual cookies onto a baking pan prepared with parchment paper. Alternatively, spoon mounds onto the tray if a piping bag is not available.
Bake: Bake for 10 minutes. Watch carefully towards the end of the baking time; the tips should be golden brown and the bottoms set. Remove from the oven and allow to cool on the tray for at least 5 minutes before serving.