To make the syrup, combine the cranberries, sugar, and cranberry juice and bring to a boil over medium heat. Reduce the heat to a simmer and cook 5 minutes.
Strain the syrup through a fine-mesh sieve, pressing the cranberries down to extract all their juice and pulp.
Pour the liquid back into the pan you made it in, and put over medium heat. Let it boil for about 3 minutes, swirling it every now and again to make sure it doesn’t start to burn around the edges. You want the consistency to be a little thick, kind of like runny honey, so if it’s not quite thick enough reduce the heat to low and just let it simmer for another 1 – 2 minutes.
Shut off the heat, and whisk in the Cointreau. Let it cool completely to room temperature before drizzling all over the cake just before serving. You can make the syrup in advance and keep it in the fridge—just let it come to room temperature and whisk it a little before pouring over the cake.