Preheat freezer to -18°C (0°F) for optimal freezing conditions

Combine water and granulated sugar in a medium saucepan, heating over medium heat, stirring occasionally, until sugar dissolves

Bring mixture to a boil, then reduce heat to medium-low and simmer for 5 minutes

Remove from heat and stir in freshly squeezed lime juice and chopped fresh mint leaves

Let mixture steep for 10 minutes, allowing flavors to meld

Strain mixture through a fine-mesh sieve into a clean container, discarding mint leaves

Chill mixture in the refrigerator until cooled to 4°C (39°F)

Pour mixture into an ice cream maker and churn according to manufacturer's instructions

Freeze sorbet for at least 2 hours, or until firm and scoopable, stirring every 30 minutes to ensure even freezing

Scoop and serve immediately, garnished with additional fresh mint leaves if desired