In a shaker, combine all ingredients except the bitters and shake without ice. Then add ice and shake again, vigorously, for at least 5 seconds. Strain into a coupe and allow to settle for just a minute.
Garnish with drops of Peychaud's bitters. (To make a garnish like what you see above, Make a line or a half-moon of dots, then drag a barspoon or toothpick through them to create your desired effect.)