Slice the peaches in half and remove the pits.
Cut the unpeeled peaches into small chunks and cook them with the water in a medium, nonreactive saucepan, covered, over medium heat, stirring occasionally, until they’re soft and cooked through, about 10 minutes. Add a bit more water if necessary during cooking.
Remove from the heat and stir in the sugar. Let cool to room temperature. When cool, purée the mixture in a blender or food processor until smooth. Stir in the kirsch or lemon juice.
Chill the mixture thoroughly for several hours, then freeze it in your ice cream maker according to the manufacturer’s instructions.
When ready to serve, allow sorbet to soften slightly before eating for sheer and utter peachy perfection.