Add mezcal, amaro, pomegranate juice, port, and agave to a pint glass or cocktail mixing glass filled with ice.
Stir well to combine all ingredients.
Strain into two coupe glasses that have been rimmed with turbinado sugar. I like to rim just a thick section on one side of the glasses as you see in the photos. Make sure you divide the cocktail evenly between the two glasses!
Garnish each cocktail with a sprig of time and, using a kitchen torch, char the ends of the rosemary sprigs so they are smoking.
Serve immediately.