Chill a rocks glass with ice or place it in the freezer for 5 to 10 minutes.
Place the sugar cube in another rocks glass and add the Peychaud’s bitters. Muddle the sugar cube with the bitters until the sugar dissolves. Add the rye whiskey to this glass and mix well to combine.
Remove the ice from the chilled glass and add the absinthe. Swirl the absinthe to coat the inside of the glass and discard anything that remains. Pour the rye whiskey mixture into the chilled glass.
Garnish with a lemon twist.
Notes
Chill the glass. There is no ice in this classic cocktail recipe, so you will need to chill the glass first. Either fill the rocks glass with ice to chill it or simply place the empty glass in the freezer for 5 to 10 minutes.
In place of a sugar cube, you can use 1 teaspoon of granulated sugar or 1 teaspoon of a strong simple syrup (2:1 ratio of sugar to water).
Add Angostura bitters: Some recipes also add a dash of Angostura bitters for even more complexity and herbal flavor.