Preheat the oven to 275 degrees F (135 degrees C). Line 2 baking sheets with parchment paper.

Beat together egg whites and sugar in a large bowl with an electric mixer until soft and creamy, about 2 minutes. Stir in 2 cups shredded coconut and gluten-free flour slowly until combined into a dough.

Shape dough into walnut-sized balls. Roll balls in remaining 1/2 cup shredded coconut until evenly coated and place 2 inches apart on the prepared baking sheets.

Bake in the preheated oven until lightly golden, about 30 minutes. Cool on the baking sheets for 1 minute before removing to a wire rack to cool completely.