Fill a rocks glass with 1 cup ice and let it chill for about 5 minutes. Discard the ice.
In a cocktail shaker, mash together the Peychaud's Bitters, Angostura Bitters, and sugar cube using a cocktail muddler. Add 1 cup ice and the whiskey; stir until well-chilled.
Strain the chilled mixture into the prepared rocks glass.
Gently twist the lemon peel over the surface of the cocktail to release its essence, then discard it.
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