Add peaches, water and half of the sugar to a saucepan and cook over medium heat, stirring often, until mixture becomes thick and jammy. This should take at least 20-30 minutes. Once thick, put in the freezer for 15 minutes to cool. Remove and stir, then strain through a sieve to remove any stringy parts into a bowl.
Prepare base
Add the milk, cream and vanilla to the peaches and thoroughly combine. In a larger bowl add the egg yolks, salt and remaining ½ cup of sugar and whisk until thoroughly combined and egg yolks have become a pale, creamy yellow. Pour the milk and peach mixture into the egg mixture and whisk thoroughly to combine. The sugar should be dissolved.
Pour base into gelato maker and run for about 40 minutes or until thick and creamy.