In a cocktail shaker, combine the whiskey or mezcal, lemon juice, orange juice, and rosemary simple syrup.
Add the egg white.
Dry shake (shake without ice) vigorously to emulsify the egg white and create a frothy texture.
Add ice to the shaker and shake again until the mixture is well chilled.
Strain into a chilled coupe glass.
Briefly flame a sprig of rosemary with a lighter and place it on the drink to garnish, allowing the smoke to infuse the cocktail.