Place basil leaves in the shaker and lightly muddle.
Add vodka (or gin), triple sec or vermouth, orange juice, simple syrup, and bitters.
Fill shaker with ice and shake firmly for about 15 seconds.
Strain into a chilled martini glass.
Garnish with an orange peel twist or basil sprig. Serve chilled.
Notes
Use vodka for a cleaner profile, gin for more herbal notes. Fresh orange juice makes a big difference. Adjust sweetness and bitters to taste. Double strain for clarity if desired.