Make sure the homemade coconut milk is fully liquid and near room temperature. Put the coconut milk, water, raw honey, homemade vanilla, cinnamon, ginger, cloves, and cardamom in a glass-vessel blender. Blend for about 10 seconds, only until the honey disappears into the liquid and the fine spice flecks are evenly suspended.
Use an ice cream maker cylinder that has frozen upright overnight on the freezer's coldest setting. Assemble the maker according to its directions, seat the cylinder fully in its base, install the dasher, add the blended base, and churn to the manufacturer's endpoint. The thickened base should mound softly instead of immediately leveling like liquid.
Serve immediately for a soft texture. For firmer scoops, transfer the ice cream to a pre-chilled glass or ceramic dish, cover, and freeze it further. Test the center for scoopability instead of assigning one fixed extra-freezing time.