The Modern Sazerac Cocktail Recipe

Sazerac is New Orleans's first cocktail, concocted in the 1830s. And it's the city's only official cocktail.
As discussed in my Sazerac: New Orleans's Favorite Cocktail podcast episode, there are two main ways to make and enjoy an authentic Sazerac. The Original way. And the modern way, as detailed below.
The Modern Sazerac Recipe
1 sugar cube
1½ oz. rye whiskey
3 dashes Peychaud's Bitters
¼ oz. Herbsaint
fresh lemon peel
Start with 2 Old Fashioned glasses.
Fill the first glass with ice.
Place a sugar cube in the second glass.
Add Peychaud's Bitters into the second glass. Muddle it with the sugar till it forms a paste.
Add in rye whiskey, then stir.
Remove the ice from the first glass.
Pour Herbsaint into the first glass.
Move and twirl the first glass to coat the inside with Herbsaint.
Pour out any remaining Herbsaint present in the first glass.
Pour the whiskey-bitters mixture that's in the second glass into the first glass.
Hold a lemon peel / twist over the first glass, and squeeze out some of the oils.
Rub the lemon peel's underbelly 360-degrees around the glass's rim.
Enjoy!