Combine cardamom, coconut milk, sugar, 1 1/2 teaspoon rum, and vanilla extract in a pot. Simmer mixture over low heat, stirring occasionally, about 20 minutes. Remove mixture from stove and stir in remaining rum.
Pour mixture through a strainer over a freezer-safe container to catch the cardamom pods; discard. Cover the container and freeze until firm, 5 hours to overnight.