In a medium saucepan, combine the water and sugar. Heat over medium heat, stirring until the sugar is completely dissolved. Remove from heat and let cool.

In a blender or food processor, add the chopped peaches, cooled sugar syrup, lemon juice, and vanilla extract. Blend until smooth.

Pour the peach mixture into a shallow dish and place it in the freezer. Freeze for about 2 hours, or until the edges start to harden.

Remove the dish from the freezer and use a fork to scrape and stir the mixture, breaking up any ice crystals. Return to the freezer for another 2 hours.

Before serving, let the sorbet sit at room temperature for about 5 minutes to soften slightly. Scoop into bowls and enjoy!