Peel and core the apples, place them in a large saucepan with 2 tablespoons of water and cook for 20 minutes over low to medium heat. Once the apples are very soft, place the mixture into a sieve or colander and allow the juice to drain into a bowl (this can take up to 3 hours).
Wash and finely chop the mint leaves, add them plus 1¾ pints (1 litre) of water to a saucepan and bring to the boil. Remove the pan from the heat and set aside for 10 minutes to allow the liquid to cool a little.
Add the strained apple juice to the pan and stir in the sugar. Stir well, then bring back to the boil. Reduce the heat and simmer gently for 40 minutes, stirring regularly. Pour into sterilized jars and (optionally) drop a small sprig of washed rosemary into each jar before sealing.