In a food processor, process the zest, sugar, and salt until damp. While the machine is running, add orange juice and lemon juice. Process mixture until sugar has dissolved, about 1 minute. Strain the mixture through a fine-mesh strainer, stir in vodka, and cover with plastic wrap. Chill in freezer until very cold (40 degrees) about 30 to 60 minutes.
When the mixture is cold, whip the heavy cream in a medium bowl with a whisk until soft peaks have formed. Whisking constantly, add juice mixture in a steady stream against the inside edge of the bowl. Start ice cream maker and add the juice-cream mixture. Mix until sherbet has the consistency of soft serve ice cream, about 25 to 30 minutes.
Remove from ice cream machine canister and transfer to an airtight container. Freeze until firm, at least 3 hours.