Refrigerate or freeze a rocks or old-fashioned glass for at least 5 minutes.
Place 1 granulated sugar cube or 1 teaspoon granulated sugar, 2 ounces rye whiskey, and ¼ teaspoon Peychaud’s bitters in a cocktail shaker or mixing glass. Stir until the sugar is dissolved. Add enough ice to fill the mixing glass halfway, and stir until thoroughly chilled, about 15 seconds.
Rinse the glass with Herbsaint or absinthe: Place ¼ ounce in the chilled glass, swirl to coat the glass, then pour it out. Pour the cocktail through a strainer into the glass.
Peel a 3-inch-long strip of zest from 1 medium lemon with a vegetable peeler. Twist the zest into a spiral over the cocktail to release the oils. Garnish with the lemon twist.