Use a blender to mix the yoghurt, oil, salt, nutritional yeast flakes, and water until thoroughly combined.
Set aside for 24 hours to culture; it will thicken a little, taste a bit more sour, and look a little curdled, depending on how warm your home is.
Once it's cultured, pour the yoghurt into a heavy-bottomed, medium-size pan, and whisk in the tapioca flour, carrageenan, and lactic acid until smooth.
Cut six pieces of cling film, about 30cm (12”) long, and lay them out on the counter or table.
Add a couple of teaspoons of salt to a large bowl of iced water to make a brine.
Cook the mozzarella mixture over a medium heat, stirring all the time, until it becomes thick and lumpy. This should take around 5-7 minutes.
Keep cooking and stirring for another 5 mins until the mixture becomes smooth and glossy, and starts to come away from the sides of the pan.
Remove the pan from the heat, and place a few scoops of mozzarella onto the centre of a piece of cling film. Flip each side over to cover the cheese, then carefully pick the whole thing up by the ends of the wrap, and twirl to make a sausage shape. Tie each end together to form a ball, and then drop into the brine.
Repeat for the rest of the mixture.
Leave the mozzarella in the brine for around 30 mins to cool (the longer you leave the it in, the firmer it will become).
Unwrap, and use straight away, or store (unwrapped) in some of the brine in an airtight container or plastic bag in the 'fridge for up to a week.
You can use any neutral oil - e.g. canola, sunflower, rice bran - but as a general rule, I prefer to use coconut oil for most of my cooking (both refined and virgin). This is just my personal preference - the mozzarella isn't going to be affected, either by taste or texture, by the oil you use, unless you use a strongly-flavoured one.
If you do use coconut oil however, do make sure you use the refined stuff - unless you want your mozz to taste of coconut. I've tried it, it's a singularly odd experience. And not one I recommend!