Combine rye whiskey, sweet vermouth, Bénédictine, absinthe, and Peychaud's bitters in a mixing glass.
Add ice and stir for approximately 30 seconds until well chilled and diluted.
Fine strain into a chilled coupe glass.
Garnish with skewered maraschino cherries.
La Louisiane dates to at least the 1930s, associated with the Restaurant de la Louisiane in New Orleans. The absinthe quantity is deliberately small - just a rinse-level presence - so resist the urge to increase it, as it can quickly dominate the balance.
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