Pour 1 drop of bitters into each of 2 tall stemmed cocktail glasses and swirl to coat the inside of the glass. Pour any remaining bitters from the glasses. Rub the lemon peel over the rims of each glass and place inside the glass.
In a cocktail shaker, combine the bourbon, vermouth, and 6 cubes of ice. Shake well until mixed and chilled, about 30 seconds. Strain and divide the mixture between the 2 glasses. Garnish each glass with stemmed cherry and serve.