Start by chilling an old-fashioned glass.

In a mixing glass, muddle the sugar cube with Peychaud's Bitters.

Add rye whiskey and fill the mixing glass with ice.

Stir well until the mixture is well-chilled.

Rinse the chilled glass with absinthe, discarding the excess.

Strain the whiskey mixture into the glass.

Garnish with a twist of lemon peel.