In a medium saucepan, combine the water and sugar. Heat over medium heat, stirring until the sugar dissolves completely. Remove from heat and let cool.
In a blender or food processor, combine the chopped plums, cardamom, lemon juice, and a pinch of salt. Blend until smooth.
Once the sugar water has cooled, add it to the plum mixture and blend again until well combined.
Pour the mixture into a shallow dish and place it in the freezer. Freeze for about 2 hours, then stir with a fork to break up any ice crystals.
Return to the freezer and repeat the stirring process every 30 minutes for about 2-3 hours, or until the sorbet is firm and fluffy.
Once ready, scoop the sorbet into bowls and serve immediately.