Martha's riff on the beloved New Orleans cocktail mixes a base of bourbon or rye with sugar, orange bitters, and anise-flavored liqueur. Absinthe is traditional, but you can also use sambuca or Pernod.
Place sugar cube and 2 teaspoons water in a cocktail shaker; stir to dissolve. Add bourbon and bitters, fill with ice, and stir to chill.
Pour liqueur into a rocks glass and swirl to coat; pour out excess. Strain bourbon mixture into glass. Twist lemon peel and rub around rim of glass (do not add to drink).