Place the apple juice and spices in a saucepan over a medium heat. Bring to a simmer and reduce to low. Simmer for 20 to 30 minutes until the juice has reduced by almost half. Remove from the heat and leave until completely cool.
Pour the mulled apple juice into a jug and add the apple slices, ice and sparkling (soda) water. Add sprigs of rosemary to the serving glasses and serve.