To make the simple syrup:
Combine all ingredients in a saucepan over medium heat. Bring to a simmer.
Reduce heat to low and simmer for 15 minutes, stirring occasionally.
Remove from heat and allow to “steep” for 30 minutes.
Pour through a strainer and refrigerate until cold.
To make the mule:
Add the vodka, pomegranate syrup + lime juice to a cup. Stir it all together.
Add ice. Fill to the top with ginger beer and mix well.
Garnish with frozen pomegranate seeds and fresh rosemary.