The Sazerac is a local variation of a cognac or whiskey cocktail originally from New Orleans, named for the Sazerac de Forge et Fils brand of cognac brandy. The drink is most traditionally a combination of cognac or rye whiskey, absinthe, Peychaud's Bitters, and sugar. The cocktail, which is a close cousin to the Old Fashioned, has been kicking around in one form or another since as early as 1838 and was trademarked in 1900 by Sazerac Co.
Chill an old-fashioned glass by filling it with ice. Let it sit while you prepare the rest of the drink.
In a mixing glass, soak the sugar cube with the bitters and muddle to crush the cube.
Add the rye and cognac, fill the mixing glass with ice and stir until well-chilled.
Strain into the prepared glass.