From what i understand "cottage cheese" is a cheese made from milk treated with rennet, lightly strained, and mixed with a little bit of cream. I'm sure there's regional variation in the terminology and process.

From like 2 minutes of searching online, I seems like what people call "dry cottage cheese" is basically just what I described. Heat milk, acidify it, and strain. Typically what I do is strain it with a cloth until it's fairly dry, then I'll mix back in some of the whey until I get the texture I like.

The fancier version involves fermentation with bacterial cultures to create the necessary acid, but that's not something you are going to do with a half jug of milk you want to just use up before it goes bad.