Line a colander with a double layer of cheesecloth or a single layer of butter muslin.
Pour the milk into a large, heavy-bottomed kettle, and bring it to a boil over medium heat. Stir it frequently to keep the milk from scorching. When it comes to a boil, immediately reduce the heat to low, and stir in the vinegar. The milk should immediately separate into curds and whey. If it does not separate, add a bit more vinegar one tablespoon at a time until you see the milk solids coagulate into curds swimming within the thin greenish blue whey.
Pour the curds and whey into the lined colander. Rinse them gently with cool water. Tie up the cheesecloth, and press it a bit with your hands to remove excess whey. Let the cheesecloth hang for 1 to 2 hours, then open it up and chop it coarsely. Store in the fridge for up to a week.