In a small saucepan, simmer sugar, basil stems and water over medium heat until sugar dissolves. Let cool. Meanwhile, set aside 6 strawberries and 12 small basil leaves for garnish.
Remove basil stems from the cooled sugar syrup and pour syrup into a blender. Add basil leaves, strawberries and vinegar and blend until smooth.
Strain out seeds and pulp, pour into a shallow metal pan and freeze. Every 30 min. stir and scrape the mixture with a fork, repeating 5 to 6 times until it has frozen into crystals. Scoop into bowls and garnish with reserved basil leaves and strawberries.