I was complaining to @RobertSimonson about the disappearance of the Absinthe Suissesse (amongst other names) from the New Orleans brunch drinks menus, and did a little digging.
I’m unclear which hemisphere this drink actually arose in. It seems like it could have an antecedent in the “Italian” style of drinking absinthe, which tempers the absinthe with liqueur(s). One example of many similar:
On the other hand, there are plenty of American “Absinthe Cocktail” and “Absinthe Frappé” recipes that use anisette as a sweetener.
The earliest Absinthe Suissesse recipe I’ve found so far is from Frank Newman (1904, not in the 1900 edition). Here we see an egg white and seltzer (and we’ll disregard the grenadine).
Mahoney (1905, at least) gives us an Absinthe Cocktail with an egg white.
The first reference to orgeat I’ve found is Seutter, Der Mixologist (1909), as the sweetener a simple frappé.
(Same as Absinthe Frappé, but add a half liqueur glass of orgeat)
Lexicon der Getranke (1913) keeps the orgeat and makes it fizzy.
(Fill the shaker half full with ice, 1 liqueur glass of absinthe, 4 dashes of anisette, 1/2 liqueur glass of orgeat syrup, shake, strain the fizz glass and fill up with seltzer.)
Beverages de Luxe (1914) has something degenerate-looking, but references the St. Charles Hotel.
By the time we get to Stanley Clisby Arthur (1937), the drink is clearly going sideways.
Speaking for myself, the essence of the drink is orgeat (as sweetener) and the silver fizz format (egg white, seltzer). I see no problem also incorporating pastis (particularly Herbsaint) or anisette, if useful, but you’re using a similarly-flavored liqueur to the base spirit. Orgeat adds the more distinctive, complementary character.
Cream is also a thing, but it seems newer, possibly a crossover from the Ramos Fizz. Here’s Chuck Taggart’s page on the drink from 2008. The recipe he gives is:
1-1/2 ounces absinthe (substitute Herbsaint or pastis if you can’t find absinthe near you)
1/2 ounce orgeat
1 egg white
1 dash orange flower water (optional)
2 ounces heavy cream
1/2 cup crushed or cubed ice
Serve either shaken or blended; old traditional method is to shake vigorously for 15 seconds with crushed ice, or blend with cubed ice. Serve in an Old Fashioned glass.
I think there’s a similar, semi-contemporary New Orleans recipe in Obituary Cocktail (2011), but I don’t have it handy.
Anyway, I would love to see a really inspired 2022 interpretation.