In a pint glass, add brown sugar, Peychaud’s Aperitivo, and Angostura bitters. Muddle until sugar is mostly dissolved, 20 to 30 times. Add rye and rum, and set aside.
Discard ice from lowball glass, and add Legendre Herbsaint. Swirl until glass is fragrant; discard remaining liquid.
Add ice to brown sugar mixture, and stir vigorously until drink is very cold, 30 seconds to 1 minute. Strain into lowball glass. Garnish with lemon peel, if desired.
Recipe by Louisiana Cookin' at https://louisianacookin.com/split-base-rye-rum-sazerac/