I forget the details of the process, but you can use soured milk to make cheese, in fact it was something of the original starter. When I've made my cheese from kefir, which is simply a different cultured milk product, I waited for it to thicken, clump, and/or separate, then I poured it into a double layered cheese cloth, squeezed out all the whey that I could, and suspended it over a bowl to drip out the rest at its own pace, which could take a day or two. When drained, you can just salt it and leave it in a bowl in the fridge to mellow a little while, then eat it like a yogurt cheese.
Or, if you want to get fancy, you can speed along the separation with a few drops of rennet or half a tablet if you have the solid form (ground, thank you), then you double layer the cheesecloth in a bamboo steamer, pour the culture in, wrap the cloth over the top of it, put a wood disk or plate in that just about fills the bamboo steamer, and stack weights on top. The heavier the weights, the firmer the "cheese," this produces. You'd need a lot of weight and time to produce a hard cheese, then you'd want to let it sit in a brine awhile.
By the way, the whey is quite usable wherever water is called for in a recipe, or if you can heat it well below a boil, tiny curds will precipitate out of it which, when drained, will be ricotta (this twice cooked whey is still useful for cooking, baking, and soaking flour).
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AnnaArcturus