In a cocktail shaker, add the basil and the sugar cube. Muddle them together in the bottom of the shaker until the basil is fragrant. Pour in the green tea, lime juice, rum and honey. Stir until well mixed. Carefully pour the mixture into a highball glass filled with ice. Garnish the cocktail with the lime wedge and a basil leaf.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.