Combine water, sugar, and mint leaves in a saucepan.

Heat over medium heat, stirring until sugar dissolves.

Bring to a boil, then reduce heat and simmer for 3-5 minutes to extract mint flavor.

Set aside to cool.

Strain out the mint leaves.

Pour the cooled mint mixture, lime zest, lime juice, sparkling water, and rum (if using) into a bowl.

Mix well.

Pour into an ice cream maker.

Freeze according to the manufacturer's instructions.

Serve immediately for a softer texture, or freeze in a sealed container for a harder sorbet.

Let hard-frozen sorbet thaw a few minutes before serving.