Pour most of the coconut milk into a medium pot, reserving a few tablespoons of the clear liquid to pour into a small bowl.
Add arrowroot powder to the bowl and whisk with a fork until perfectly smooth. Pour mixture into pot.
Add corn syrup and sugar to pot.
Set pot over medium heat. Whisk until contents are perfectly smooth, and then from time to time.
Bring mixture to a gentle boil, then boil for 90 seconds, whisking slowly every 30 seconds or so. Remove from heat.
Place cubed mango into blender along with vodka, vanilla, cardamom, and salt. Pour in coconut milk mixture.
Blend until perfectly smooth, starting on low and ending on high. If you don't have an ice cream maker with a condenser (or if you do and prefer a shorter churn time), chill mixture before proceeding.
Pour contents into ice cream maker and churn according to manufacturer’s instructions.
Ice cream is ready to eat if you like a softer consistency, or you can transfer it to an airtight container, place a piece of parchment or plastic wrap directly on the surface before positioning the lid, and freeze for several hours to firm it up to scoopable consistency.