In a cocktail shaker, muddle the 3 basil leaves with the Fennel Syrup. Add the lime juice, then fill the shaker with ice and shake well. Fine-strain into a chilled rocks glass over the large ice cube and garnish with the basil sprig.
Fennel Syrup: In a saucepan, boil 4 ounces of water. Remove from the heat, add 1/2 cup cubed fennel (1/2-inch pieces cut from 1/2 small bulb) and let steep for 6 minutes. Remove and discard the fennel. Add 1/2 cup sugar to the saucepan and bring to a boil, stirring until dissolved. Remove from the heat, let cool and transfer the syrup to a jar. Refrigerate for up to 2 weeks. Makes about 6 ounces.
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