In a heatproof bowl, mix together the coconut, egg whites, and powdered or granulated sugar.
If you have a double boiler, now is the time to use it. If not, create your own by filling a stainless steel saucepan with about 3 inches of water to form the base. Place the heatproof bowl holding the coconut mixture over the saucepan and cook over medium heat for 15 minutes, stirring occasionally. Ensure that the water remains at a gentle simmer and does not boil. At this point, the mixture will become loose and sticky. Remove the bowl from the heat, cover it directly with plastic wrap, and refrigerate overnight, or for at least 6 hours.
Preheat the oven to 170°C/340°F.
Use a spoon to scoop the coconut dough into 10 equal mounds. Slightly dampen your hands to shape the mounds into balls, then gently flatten each ball into a disc about 2.5 cm (1 inch) thick.
Transfer the cookies to a baking sheet lined with parchment paper, spacing them 2 inches (5 cm) apart.
Place a maraschino cherry on top of five of the cookies.
Bake for 15 to 17 minutes until golden, yet soft to the touch.
Cool the cookies on the baking sheet for a few minutes, then transfer them to a wire rack to cool completely.
Spread the jam on the flat bottom of the five cookies without maraschino cherries, then top with the remaining cookies. You now have a beautiful and delicious treat!