To prepare a Sazerac cocktail, start by chilling an Old Fashioned glass. Place a sugar cube in the chilled glass and add Peychaud's bitters. Muddle with water until dissolved. Rinse the glass with absinthe, swirling to coat, then discard excess. Mix rye whiskey and ice in a mixing glass and stir until chilled. Strain the mix into the prepared glass and garnish with a lemon twist.