Step 1

Place coconut milk and coconut cream in the refrigerator.

Step 2

Place water and rice in a blender. Blend until rice is coarsely ground. Pulse until rice is finely ground. Pour mixture into a jar or bowl. Add vanilla bean halves and cinnamon stick pieces. Cover and refrigerate, 8 hours to overnight.

Step 3

Strain rice 'milk' mixture through cheesecloth. Scrape vanilla seeds from the pod and add to the milk. Discard rice pulp and cinnamon stick pieces.

Step 4

Blend strained rice milk, coconut milk, coconut cream, brown rice syrup, and rum until well combined.

Step 5

Pour into an ice cream maker and freeze according to manufacturer's directions, 15 to 20 minutes. Freeze the mixture for 2 to 3 hours before serving.