In a small saucepan, combine the coconut milk, one and a half teaspoons of the honey, ginger, cinnamon stick, and a pinch of salt. Bring to a boil over medium heat. Reduce the heat and simmer for ten minutes, whisking frequently to prevent the milk from burning. Remove from the heat.
Wearing rubber gloves to prevent staining your hands squeeze the beet over the saucepan to release the juice. Discard the pulp. Taste and add more honey, if desired.
Remove the cinnamon stick and transfer the liquid to a high-speed blender. Add the ghee and blend on high speed for 30 seconds. Pour into two cups and sprinkle with a pinch of nutmeg.