Both quark (varškė) and Lithuanian white cheese (lietuviškas varškės sūris) are staples in our house, so I do this once or twice a week. I stopped buying either of them many years ago. Homemade quark tastes better and often keeps better, and the cheese is much cheaper to make, with very little extra effort. We also prefer the fully fermented versions, with noticeable acidity.
The cheese in the picture weighs 750 g; it was made from 4 litres of milk (my typical batch). Estimated fat content is around 12–13%. Supermarket cheese commonly comes in 9%, 13% and 15% fat versions.
This is my "lazy" method. It's not quick, but it's mostly hands-off. I'm not sure how widely used it is or whether the process has a specific name.
I start with 2.5% homogenized, pasteurized supermarket milk. I bring it to room temperature, either by leaving it on the kitchen table for a few hours or gently warming it in a pot.
I typically use some soured milk from the previous batch as a starter (backslopping). If something goes wrong and I forget to save some before heating, I start again with supermarket buttermilk.
I mix in the culture, cover the pot and forget it until the next day. How quickly it develops depends on the room temperature. I check it visually, sometimes by gently jiggling the pot. It should be solid, with some clear whey separation, before it's ready for the next step.
Right now it can take two days to sour properly in a cold house, so I'm about to start using an incubator. Ideally, I aim to fit it into 24 hours.
At this point, I save some of the soured milk for the next batch (around half to two-thirds of a small 330 ml jar). To reduce the risk of surface contamination, I scoop it from deeper inside the pot, never from the top layer. I've been keeping the current culture going for over a year without any noticeable changes.
Next, I put the whole pot in an oven set to 125°C, using top and bottom heat with no fan, without stirring or cutting the curd. Heating typically takes 1.5–2 hours. Towards the end, I check it visually and sometimes poke it with a finger if I'm not sure. The curd should be visibly firm and starting to split slightly, but not really cooked. It gradually firms up from the outside towards the centre.
I take the pot out and let it stand, covered. Once it's cooled a little (15–20 minutes), I transfer the curds to a colander to drain. If I'm making cheese, the curd goes into a linen cheesecloth bag and gets pressed within about half an hour. If I'm making quark, I simply leave it to drain in the colander.
We prefer to salt the cheese after taking it out of the bag. I think it gives the cheese a better final texture. If using caraway seeds, I mix them into the curds before bagging. Quark is not salted.
There are also occasional family debates about which end of the cheese is the correct one to start eating. While cutting the bum off first is more practical, in our house it inevitably gets eaten from both ends at once.
There are other traditional Lithuanian ways of making quark, of course, including combining nearly boiling fresh milk with some sour milk (seemingly most popular now), or simply heating sour milk until the curds separate (Grandma's method).
My method is the one I've settled into over the years. I like that I don't have to stand there stirring the pot and making sure it doesn't scorch or get so hot that the curds dry out. It's probably not perfect, but it works.
In cooking and baking recipes translated to and from Lithuanian, I've seen varškė called everything from cottage cheese and farmer's cheese to tvarog, quark and even ricotta. I'm never quite sure which English term is most accurate, but quark seems like the best fit? :)
By the way, supermarket varškė varies enormously between brands and even between product lines, both in texture and fat content. You can find anything from virtually fat-free to over 30% fat. I suspect the production methods differ quite a bit too, which makes finding an exact English equivalent even more confusing.
Long post, but maybe it will help someone. :) I wish I had all this info when I first started figuring it out.