Preheat oven to 350 degrees. Lightly grease 2 baking sheets with butter (or line with silicone baking mats).
Cream together the butter and sugar until pale and fluffy, about 2 minutes. Add the egg yolk, vanilla, and lemon zest, and mix well. Stir in the flour, add the cherries and mix with your hands until it forms a soft dough.
Lightly flour a surface, roll out the dough to a ¼ inch thickness and cut into 3 inch rounds with a cookie cutter. Cut out the center of each cookie with a 1 inch cookie cutter. Place the rings on the prepared baking sheets. Re-roll any trimmings and cut more cookies. Bake the cookies in the preheated oven for 15 minutes or until they are firm and just beginning to color. Let cool on baking sheets for 5 minutes then transfer to a wire rack to finish cooling.
Mix the confectioners’ sugar with lemon juice and maraschino cherry juice until it becomes a smooth paste. It may take a little less or more lemon juice, so start with less and add a little at a time. Drizzle over the cooled cookies and let stand until the icing sets, about 30 minutes.