Chill an Old-Fashioned glass by packing it with ice or placing in the freezer.

In a second Old-Fashioned glass add the sugar cube and the Peychaud's Bitters, then crush the sugar cube.

Add the Rye Whiskey to the second glass containing the Peychaud's Bitters and sugar.

Empty the ice from the first glass and coat the glass with the absinthe, then discard the remaining absinthe

Empty the whiskey/bitters/sugar mixture from the second glass into the first glass and garnish with lemon peel