Can I make my own cheese by letting a glass of milk sit on the counter for a week or so?

Would a glass of milk, (or maybe less, say a couple of ounces) ever turn into edible cheese? How long would it take? How foul would it be?

I left an inch or so of 2% milk in a glass on my counter last night; by this morning it was semi-solid but runny. I imagine that if I had left it out, it would have continued to change in texture.

Can I make cheese this way? How awful would it be? Or would it just be rotten foul milk?