Drain and rinse the cashews from the soaking water. Place in a high powered blender with filtered water. Blend until completely smooth and milky looking. If you've never made nut milk, keep in mind you need a high powered blender like a Vitamix in order to get the nuts blended thoroughly.
Strain by hand through a nut milk bag, a double layer of cheesecloth, or you can use a pair of cheap brand new panty hose. Cut one leg off! Pour the milk through whatever you're using over a large bowl and squeeze out the liquid by hand until the pulp is dry and there is no more liquid left.
Rinse and dry out the blender and then add the cashew milk back to the blender. Scoop the thick cream off the top of the can of coconut milk and only add that to the blender along with the remaining ingredients, except the rum! Blend until smooth. It can be served immediately or stored in a jar in the fridge for up to 7 days. You can also freeze this mixture for up to 2 months. It will separate when refrigerated or thawed from frozen but just shake it up before serving.
When ready to make the drinks, get a little bit of additional coconut sugar and place it on a plate. Wet the edges of your glass and rim the serving glasses with coconut sugar. Add ½ to 1 ounces of spiced rum per serving - depends on how strong you like it. Then top with about ¾ cups of the vegan nog. You can add coconut whip on top as well!