Combine lemon juice, 8 peach slices, and basil leaves in a cocktail shaker. Muddle for 1 minute (use a muddler or just the back of a wooden spoon). Fill shaker with ice, and add Triple Sec and bourbon. Cover and shake vigorously for 2 minutes.
Strain into ice-filled Old Fashioned glasses; garnish each with a leaf of basil and 2 peach slices. Finish with a couple dashes orange butters.