A classic, serious cocktail, with an option to add orange licorice bitters to amp up the flabor profile of the original.
Fill an Old Fashioned glass with ice and let sit as you make the drink that will go in it. (Alternatively, keep an Old Fashioned glass or two in the freezer at all times.)
In another Old Fashioned glass, add your sugar cube and dashes of bitters. Muddle with a muddler until well mixed.
Add the rye whiskey and a few ice cubes to the muddled sugar and bitters mixture and stir, letting the ice melt just a bit.
Dump the ice out of the first glass and pour in just the dash of absinthe. Hold the glass at a 90-degree angle and spin it so that the absinthe coats the inside of the chilled glass. Pour out any excess absinthe.
Stir the mix in the second glass again to ensure even distribution of any newly-melted water, then strain into the chilled, absinthe-coated glass.
Twist the lemon peel over the drink, then add to drink as garnish.