For the Cookies: Add the sugar and butter to a mixing bowl, and beat on high until creamed together. Slowly beat in the eggs, vanilla, and pomegranate juice. Once the mixture is combined, slowly mix flour and salt into the wet ingredients. Add more flour as needed so the dough doesn’t stick to the surface.
Immediately roll out the dough on floured parchment to about 1/4"thick.
Cut out shapes using cookie cutters and transfer to a parchment-lined baking sheet.
Using a small circle cookie cutter, cut out the center of every third cookie.
Bake cookies for 12 to 13 minutes. Cool on a wire rack before handling.
For the Pomegranate Icing: Using a whisk, mix the pomegranate juice and powdered sugar. Fill a piping bag with the icing. Alternatively, fill a ziplock bag and cut off the edge.
Pipe icing along the edge of one whole cookie. Place a hollow cookie on top and fill it with sprinkles. Pipe icing along the hollow cookie edge and top it with a whole cookie. Decorate the top of the cookie with more icing and sprinkles as desired. Put finished cookies in the fridge to set.