To make the basil syrup, gently heat the sugar and water until the sugar dissolves. Cook for 10 minutes until a syrup is formed.
Remove from the heat and add the basil. Blend until smooth in a processor.
For the ice cream, whip the cream until it quadruples in size. Fold in the vodka and condensed milk and whisk until firm.
Stir in the basil syrup and mix well.
Pour into a container and freeze for at least 8 hours, stirring every hour or so to keep it smooth.
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