Make the cranberry sauce:
Bring orange juice, water and sugar to a boil in a medium sauce pan. Add the cranberries and orange zest and return to a boil. Reduce the heat to low and boil gently for about 10 minutes. When most of the berries have burst, remove from heat. Cool at room temperature then chill in refrigerator.
Make the cookies:
Preheat oven to 350 degrees. Cream together butter and sugar with mixer on medium speed. Add the egg and orange extract, and mix well. Gradually add the flour and mix on low speed until just combined. Use a small cookie scoop to measure approximately one tablespoon dough. Gently roll dough into a ball and place on a baking sheet lined with parchment paper or silicone baking sheet. Make a small indentation into the center of the ball, and fill with a small scoop of cranberry sauce.
Bake for 10 minutes. Cool on a rack to room temperature, then chill in refrigerator.
Make the glaze:
Sift the powdered sugar through a strainer to remove the lumps. Whisk the sifted powdered sugar and milk together until smooth. Whisk in orange extract. Pour the glaze into a pastry bag or a small zipper bag and cut of a small part of one corner of the bag. Drizzle glaze over the cookies. The glaze will harden in 10-20 minutes.