Preheat your oven to 350°F (175°C). Do not grease your baking sheet; set it aside.
In a large bowl, cream together the softened butter, confectioners’ sugar, water, and coconut extract until the mixture is smooth and fluffy.
In a separate mixing bowl, combine the flour, oats, and salt. Gradually incorporate the dry mixture into the creamed butter mixture, blending just until a dough forms.
Scoop out approximately one tablespoon of dough at a time. Gently flatten each portion, nestle a maraschino cherry in the center, then encase the cherry entirely with dough. Roll into a smooth ball and place it onto the prepared baking sheet.
Transfer the sheet to the oven and bake for 17 to 19 minutes, or until the undersides of the cookies are lightly golden. Once baked, allow them to cool completely on a wire rack.
In a small bowl, whisk together the powdered sugar and milk to form a fluid glaze. Add extra milk if needed to reach a dipping consistency. Dip each cooled cookie into the glaze, then immediately roll it in the finely chopped coconut.
Allow the glazed cookies to rest at room temperature until the coating sets. Store the finished treats in a sealed container to maintain freshness.