In large bowl whisk together ginger beer and sugar till foam subsides and sugar is completely dissolved, about 3 minutes. Whisk in coconut milk, salt, and ginger.
Transfer base to ice cream maker and churn according to manufacturer's instructions. When sorbet is finished, slowly pour in rum and churn 1 minute longer. Transfer to airtight container and freeze for 2 to 3 hours, or until firm and scoopable. For serving, garnish with lime zest and, if you like, an additional tablespoon of rum per bowl.
