Cut the pomegranate in half and extract the arils. Place the seeds in a blender or food processor and blend until frothy. Strain into a bowl or large measuring cup.
To make the simple syrup: Using a small saucepan, bring the sugar or honey and three tablespoons of water to a boil. Remove from heat. Place 5 mint leaves and a lime wedge into a tumbler glass. Muddle, using a wooden spoon or muddler if you have one. Pour in the pomegranate "juice." Add the rum if you're using it and 1 tablespoon of the simple syrup mixture and stir to combine.
Drop in some ice cubes and top off with club soda. Garnish with a lime wedge. Cheers!
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