- Chill an Old Fashioned glass by placing it in the freezer or filling it with ice water.
- In a mixing glass, add 2 sugar cubes and a few dashes of Peychaud's bitters. Muddle until the sugar is dissolved.
- Add 2 ounces of Armagnac to the mixing glass with ice. Stir well until chilled.
- Discard ice from the chilled Old Fashioned glass and rinse it with absinthe (or absinthe substitute), swirling to coat the inside and then discarding the excess.
- Strain the chilled Armagnac mixture into the prepared glass.
- Garnish with a lemon twist, expressing the oils over the cocktail before placing it on the rim.