Pour mezcal, lime juice, agave, apple cider, and a few pinches of sea salt into cocktail shaker. Stir to incorporate agave.
Pinch off a few rosemary leaves and muddle into liquid for just a few seconds, crushing against base of cocktail shaker to release flavor.
Add ice, cap cocktail shaker, and shake. Pour through strainer into glasses with large ice cube and garnish with rosemary sprigs and apple slices.