1. Add the basil leaves and lemon juice to a cocktail shaker and muddle 10 times, or until the basil has broken down. Add the lemon peels and muddle 5 more times. Let sit for 2 to 3 minutes to steep.
2. Fill a martini glass with ice water to chill. Add vodka or gin, orange liqueur, and agave nectar into the cocktail shaker and fill with ice. Seal and shake until the shaker is cold, about 1 minute. Dump out the ice water from the martini glass, strain the martini into the chilled glass, and garnish with a lemon peel twist.

Tip: For a traditional lemon drop martini, omit the basil.