Make the citrus-infused vermouth: In a large container, combine the lemon and lime zests with the vermouth. Set aside overnight, then strain through a fine-mesh strainer. Return the mixture to a bottle and refrigerate until ready to use.
Make the cocktail: Fill a mixing glass with ice and add the apple brandy, citrus-infused vermouth, bitters, pomegranate molasses and salt. Stir until chilled and strain into a chilled coupe glass.