Crack open the cardamom pods and grind the seeds using a spice grinder or mortar and pestle.
Add the sugar and water to a small saucepan over medium heat until sugar dissolves. Add the vanilla extract and ground cardamom and let simmer for 2 minutes before removing from heat.
Let cool to room temperature, then strain through a fine mesh strainer.
For the cocktail
Fill your glass with ice and add the vodka, pomegranate juice, lime juice, vanilla cardamom syrup, and bitters.
Give the drink a quick 10 second stir and garnish with pomegranate seeds and a sprig of fresh mint.