Place the cashews and potato into a small saucepan and cover with water. Set over high heat and bring the water to a boil.
Lower the heat and allow the water to simmer for 20 minutes.
Remove the pot from heat and drain the water.
Transfer the cashews and potato to the bowl of a food processor fitted with an s-blade. Add the garlic, miso, mustard, lemon juice, tapioca starch, white pepper, and ¼ cup of the non-dairy milk.
Blend to form a smooth paste, stopping to scrape down the sides of the bowl as needed.
Add another ¼ cup of milk and blend again, until smooth.
Add the remaining ½ cup of milk and blend again, until smooth.
Pour the wine into a medium pot and set over high heat. Bring the wine to a boil.
Lower the heat and allow the wine to simmer for 4 minutes, until reduced by about half.
Stir in the cashew mixture and bring everything back up to a simmer.
Allow the mixture to simmer for about 4 minutes, until it thickens up just a bit and becomes a bit more elastic.
Taste test and season with salt to taste, if needed.
Transfer the mixture to a fondue pot and serve with dippers of your choice.