This recipe requires an ice cream maker. Please prepare the ice cream maker ahead of time according to the manufacturer directions.
In a large bowl, whisk together the sugar, lime juice, and lime zest until the sugar is mostly dissolved.
1 cup granulated sugar, 1 cup freshly squeezed lime juice, 2 tablespoons lime zest
Add the heavy cream and milk. Continue to whisk until well combined.
1 ½ cups heavy cream, 1 ½ cups whole milk
Transfer the mixture to the prepared ice cream machine, and churn according to the manufacturer directions. Ours takes about 20 to 30 minutes. Scoop the sherbet into a freezer-safe container, cover with plastic wrap, then cover with aluminum foil.
Freeze for at least 8 hours or overnight. Allow the sherbet to sit at room temperature for about 10 minutes before serving.