Line a small bowl with compostable plastic wrap or have on hand a 1 to 2 silicone baking molds that total 4 cups (1L) in capacity.
Wash and dry a 1-quart (1L) mason jar, rinse it in boiling water, and let dry and cool to room temperature.
In a high-powered blender, combine the cashews, sauerkraut juice, yogurt, fermented tofu, and sea salt. Process on high speed until smooth and creamy, 1 or 2 minutes.
Transfer the mixture to the mason jar, cover with a lid, and place in a warm window or other location with a temperature of 70°F (21°C) or higher. Let it sit for 24 to 72 hours to ferment, until it has achieved a sharpness to your liking. (The cooler the location, the longer it will take.)
Whisk the melted coconut oil into the fermented cheese mixture until it is fully incorporated.
In a small pot, whisk together the water and agar-agar. Cover, bring to a boil over medium heat, and cook until completely dissolved and the mixture drips off your whisk like molten glass. This could take 2 to 3 minutes or longer. The agar-agar must reach about 205°F (96°C) to activate its gelling properties, so be patient.
Add the cheese mixture all at once into the agar-agar and use a whisk to mix well. Whisk the tapioca starch mixture into the pot. Continue to cook, stirring with the whisk, until it becomes as thick as cooked polenta, stretchy, and shiny.
Pour the mixture into the lined bowl or mold and refrigerate overnight to firm up. It can be used immediately, or you can let it firm up through an aging process; just wrap in wax paper or parchment and leave in the fridge for a couple of weeks until the desired hardness is achieved. (You can refrigerate it for another month after that.)