In a cocktail shaker, add the peach quarters, basil sprigs and sugar. Muddle lightly to break down the peach, but don't crush the basil too much.
Add in the whiskey and fill with ice. Shake until frosty on the outside.
Fill low-ball glasses with crushed ice and pour half the contents of the cocktail shaker into each. Top with a splash of soda water and garnish with a slice of peach and a small sprig of basil.