This recipe comes as a way to use Lillet Blanc after a Vesper, originally from Todd Thrasher of Restaurant Eve, via http://backyardbartender.blogspot.com/2011/05/blanc-lillet-blanc...)

10 basil leaves
3 ounces Lillet Blanc
1/2 oz gin
1 oz simple syrup

In a shaker, lightly muddle the basil leaves. Add the Lillet, gin and simple syrup and fill the shaker with ice. Shake and strain into a cocktail glass. Sip lovingly. Don't forget to store your Lillet in the fridge after you're done - it'll keep longer than way. (It is wine, after all.) Cheers.