Peel the peaches, slice in half, and remove pits. Cut peaches into chunks and cook them with the water in a medium, non-reactive saucepan over medium heat, covered stirring once or twice, until soft and cooked through, about 10 minutes.

Remove from the heat, stir in the sugar, then cool to room temperature.

Puree the cooked peaches and any liquid in a blender or food processor with the sour cream (or substitute), heavy cream, vanilla and lemon juice, until almost smooth but slightly chunky.

Chill the mixture thoroughly in the refrigerator, then freeze it in your ice cream maker according to the manufacturer’s instructions.