Rinse the berries and pick out any bad ones. Place in a small saucepan with the water and cook over low heat until tender, about 10 minutes. Let cool slightly and puree in a blender or food processor.

In a small bowl, mash the zest with 1 teaspoon of the sugar to release the oils. In a small saucepan, heat the half-and-half with the remaining sugar, stirring until dissolved; let cool to room temperature.

Stir in the blueberry puree, cream, sugared zest, juice, and vanilla. Transfer to a container, cover, and refrigerate until thoroughly chilled, about 3 hours.

Freeze in an ice cream maker according to the manufacturer’s instructions. When the ice cream is almost frozen, spoon in the liqueur, if desired, and chum until blended in, about 1 minute more.

Transfer to a container, cover, and freeze until firm, about 2 hours.