Deeply rooted in New Orleans history, the Sazerac began as the house cocktail at—where else?—the Sazerac bar. Over the past century, it's been mixed and remixed, but Karl Franz Williams's recipe hews to the original.
Chill a rocks glass with ice. Meanwhile, put simple syrup, bitters, and Cognac in a mixing glass. Fill with ice cubes and stir with a cocktail spoon, 15 seconds, twisting the spoon as you stir. Set aside.
Pour absinthe into the chilled rocks glass with ice and swirl around so the absinthe coats the glass. Pour out the absinthe, but keep the ice. Cover mixing glass with a strainer and pour cocktail into the rocks glass. Twist the lemon peel to release its oils, then drop into the cocktail. Serve.