Suzerac

Rinse a martini glass with absinthe, ensuring an even coat.

In a mixing glass, combine the rye, Suze, rich simple syrup, and Peychaud's Bitters.

Add ice and stir until the mixture is well-chilled.

Strain the mixture into the prepared martini glass.

Express the oils from a lemon peel over the drink, then discard the peel.