Using an old fashioned glass, pour a small amount of absinthe into the glass and use it to rinse the edges of the glass. Be sure to cover the entire inside if you can, then fill the glass with crushed ice and set it aside to chill. Once chilled, discard the ice.
In a mixing glass, add 2 dashes of Peychaud’s bitters and a sugar cube. Muddle the cube and add in the whiskey or cognac and stir.
Pour the contents into your chilled old fashioned glass, garnish with a lemon twist and serve.