1 cup sugar
1/2 cup water
2 cups buttermilk
3/4 cup milk
1/4 cup elderflower cordial
Prepare an ice-water bath. Bring sugar and water to a boil in a small saucepan, stirring to dissolve sugar. Cook until syrupy, about 2 minutes.
Mix buttermilk, milk, and cordial in a medium bowl, and whisk in sugar syrup. Place bowl in ice-water bath. Let cool completely.
Freeze mixture in an ice cream maker according to manufacturers’ directions. Transfer to a large container, and freeze until firm, about 1 hour. (Sherbet can be frozen for up to 5 days.)