- Chill an Old Fashioned glass by placing it in the freezer or filling it with ice water.
- In a separate mixing glass, muddle a sugar cube with a few dashes of Peychaud's bitters and a few dashes of Angostura bitters until dissolved.
- Add 2 ounces of rye whiskey to the mixing glass filled with ice and stir until well chilled.
- Discard the ice from the chilled Old Fashioned glass and rinse the glass with a small amount of absinthe, swirling it to coat the interior. Discard any excess absinthe.
- Strain the chilled whiskey mixture into the prepared glass.
- Express the oils from a lemon twist over the drink, then place the twist in the cocktail as garnish.