Evenly distribute ¼ cup of the pomegranate seeds in an ice cube tray, reserving the rest for garnish. Cut little equal sprigs of rosemary and place in ice cube tray along with pomegranate seeds. Fill ice cube tray to the brim with water and place in freezer until frozen.

In a small saucepan, heat pomegranate juice to near boiling, add cinnamon sticks, and simmer for 10 minutes. The mixture will reduce in volume. Remove from heat and allow to cool completely, at least 1 hour. Remove cinnamon sticks. Divide the spiced juice between 4 tall glasses; add 1 cup sparkling mineral water to each glass. Stir, and add pomegranate rosemary ice cubes. Garnish with additional pomegranate seeds, if desired.