The Obituary traces its roots to New Orleans in the 1940s, where it was served at Lafitte’s Blacksmith Shop. Once a smithy, the shop has been serving spirits since the late 18th century. It may really serve spirits – it is purported to be one of the most haunted establishments in the French Quarter!
If you don’t have absinthe, an anise liqueur like Pastis or anisette will work well in its place. Pastis is much sweeter than absinthe; you might prefer to omit it from the mix and instead swirl it around the glass, discarding the excess (this is called a “rinse”).