Once the ice cream mixture has chilled long enough, prepare the ice cream according to the manufacturer's directions on your ice cream maker. Allow the ice cream to churn until it appears thick and taffy-like (I have the cuisinart ice cream machine and it usually takes about 20 minutes of churning to get to this point).
Add the thick syrup, trying to add it in streams rather than thick blobs, if possible. Give it about 10-20 seconds to churn the ribbons of thick syrup in and then shut the machine off. Scoop the mixture into an air-tight and freezer-safe container and immediately seal it and place it in the freezer. Allow to freeze for at least 4 hours before serving.