Preheat the oven to 325°F (163°C). Line a cookie sheet with parchment paper.
If desired, pulse the shredded coconut briefly in a blender or food processor to make it finer and more uniform.
In a mixing bowl, stir together the shredded coconut and powdered sugar until well combined.
Add the egg whites and mix until a thick, sticky coconut mixture forms.
Scoop into 18 portions (about 1 to 1 1/2 tablespoons each) and shape into balls or domes. Place on the prepared cookie sheet.
Bake 15–18 minutes, until lightly golden at the edges and set on the bottom.
Cool on the pan for 10 minutes, then transfer to a rack to cool completely.
