In a small saucepan, combine sugar and water. Heat and stir mixture over medium heat until sugar is completely dissolved, 3-5 minutes. The mixture should look clear in color. Take saucepan off heat and cool.
In a blender, combine sugar mixture and add the basil leaves. Puree until there are little bits of basil remaining. Place peaches in a bowl.
An hour or two before serving pour the basil syrup over the peaches. Stir to combine and refrigerate. To serve, put a scoop of ice cream in individual bowls and ladle peaches over the ice cream.
Recipe provided and prepared by Karen Eropkin.