Make the cardamom syrup: Place the cardamom pods in a heat-proof container. In a saucepan, bring the water and sugar to a boil. Pour the liquid over the cardamom pods, then let the mixture steep overnight before straining and discarding the pods.
Make the drink: Fill a mixing glass with ice. Add the apricot nectar, bourbon and cardamom syrup and stir well. Strain into an ice-filled rocks glass, garnish with the mint sprigs and serve.