In a spare glass, mix the bourbon, the sugar syrup, and the two kinds of bitters. Make a twist of lemon peel by peeling it from a lemon with a sharp vegetable peeler. Rub firmly around the rim of a well-iced old-fashioned glass. Put the Pernod in the glass and swirl it around to coat the bottom. Add the contents of the other glass along with one ice cube. Serve.