Muddle the basil leaves, mint leaves, simple syrup, and fresh lime juice together in the cocktail shaker to release their essential oils and flavors.

Add the vodka to the muddled mixture.

Fill the shaker with ice, seal it tightly, and shake vigorously until the mixture is well-chilled.

Strain the mixture into a chilled martini glass, ensuring a smooth and clear drink without any bits of herb.