A Rum With a Vieux

Rinse the martini glass with absinthe, ensuring it is well-coated.

Combine the rhum agricole, cognac, navy strength rum, rich simple syrup, Peychaud's bitters, and Angostura bitters in a mixing glass.

Add ice to the mixing glass and stir the ingredients until well-chilled.

Strain the mixture into the prepared martini glass.

Garnish with a twist of lemon peel, expressing its oils over the drink before placing it on the rim.