Preheat the oven to 350°. Line 2 large baking sheets with parchment paper. Spread the walnuts in a pie plate and bake for about 7 minutes, until lightly toasted. Transfer the nuts to a plate to cool, then finely chop. Leave the oven on.
In a medium bowl, toss the chopped walnuts with the coconut and cinnamon. In a medium stainless-steel bowl, beat the egg whites until frothy. Gradually add the sugar and continue beating until stiff peaks form. Using a rubber spatula, fold in the coconut mixture.
Mound rounded tablespoons of the batter 1 inch apart on the prepared baking sheets and gently mold each cookie into a haystack shape. Bake for 20 to 25 minutes, or until dry to the touch and lightly browned. Transfer the baking sheets with the cookies onto wire racks and let cool completely before serving.
The cookies can be stored in an airtight container for 4 days.