Place the sugar, water, and half of the lime zest into a heavy-based pan over a low heat.
Stir until the sugar has completely dissolved, and there is no grittiness.
Turn up the heat, and allow the syrup to boil for a minute or so, to thicken.
Add the rest of the zest, the lime juice, and the mint leaves.
Set aside to cool.
Once it's cooled, strain the liquid through a fine-meshed sieve, or piece of muslin, into a freezerproof container. Freeze for an hour.
Remove the sorbet from the freezer, and whisk to break up any ice crystals.
Return to the freezer, and whisk every half an hour or so, to prevent ice crystals forming. It should take around four to five hours to set properly.
Once set, remove from the freezer 10-15 mins before you want to serve.
If desired, drizzle a glug of white rum over the top when serving.
Caster sugar in the US is also known as bar sugar or superfine granulated sugar. If you don't have any, you can grind your own in a coffee or spice mill, or small food processor attachment. A blender might work too.
Prep and cook times do not include passive time for cooling and freezing.