Preheat oven to 325 degrees. Place the coconut in a medium bowl. Wash and zest the oranges and mince the zest well. Squeeze the juice from the oranges, strain, and sprinkle half of it over the coconut. Toss well. Gradually sprinkle on more orange juice, a teaspoon at a time, tossing well with the coconut. Stop adding juice when the coconut is just moist enough to hold a snowball. Do not overmoisten. Mix in grated orange zest and set aside.

Place egg whites and salt in the bowl of an electric mixer and beat at medium speed until opaque and loosely foamy. Increase speed to high and add sugar in a slow stream down the side of the bowl, beating until stiff and shiny. Remove from machine and fold in the coconut. Drop by heaping tablespoons onto parchment lined baking sheets and form each into a little mound with moistened fingers. Bake at 325 for 1012 minutes until cookies are set and tips are browned. Remove from oven and let cool on rack in pans for 5 minutes, then use spatula to remove cookies from pans and let cool directly on rack. When cookies are cool, melt chocolate in small metal bowl over gently simmering water. Dip bottom of each cookie into melted chocolate and place on cookie sheet lined with parchment of wax paper. Allow chocolate harden and then serve.