This recipe is an adaptation of the technique for strawberry ice cream explored by Max Falkowitz when he was at Serious Eats. The better your berries, the better your ice cream will be.
To prepare the strawberries: Wash, trim the tops to remove leaves, and then quarter 1 cup (about 170g) of strawberries. Slice the quarters very thinly. Place in a mixing bowl and pour 1/2 cup (99g) of the sugar and the liquor over the berries. Mix, cover, and refrigerate for at least 2 hours, and as long as 2 days.
To make the purée: Wash, trim the tops, and slice the remaining berries, and purée in a blender until very smooth. Strain through a fine-mesh strainer to remove the seeds, then measure out 1 1/2 cups of the strained purée. Reserve any extra for another use.
Whisk the xanthan gum into the remaining 3/4 cup (149g) sugar in a large mixing bowl. Whisk in the 1 1/2 cups of purée, half-and-half, and corn syrup, whisking until fully combined. Add salt to taste and, if the mixture is too sweet, a few drops of fresh lemon juice.
Chill the base until very cold, then freeze in an ice cream maker according to the manufacturer's instructions. In the last minute of churning, retrieve the sliced strawberries from the refrigerator, drain the liquid, and add to the ice cream for the final few turns.
Transfer the ice cream to a covered container and freeze for 2 to 3 hours before serving.
