In a small saucepan, heat apple cider on low until steaming. Bring to a near boil; then remove saucepan from stove and place lid on pan.
Place butterscotch candy in a plastic sandwich bag. Crush candy using a rolling pin. Place crushed candy pieces in the bottom of an Irish coffee glass-mug.
Sprinkle brown sugar over candy pieces in the mug.
Top candy and brown sugar with hot cider leaving 1½ to 2 inches from the top of the mug. Gently stir the contents of the mug using the cinnamon stick to melt the candy. Leave cinnamon stick in the mug.
Add rum to the mug and stir again with cinnamon stick.
Float Plugrá Butter atop the prepared mug and dust with nutmeg.