First things, first. Be sure that all equipment and surfaces are clean and sterile before beginning.
Prepare the cheesecloth by rinsing it with hot water, and wringing it out. Line a colander with the cheesecloth and set aside.
Pour the milk into a large heavy-bottomed pot and place over medium high heat to warm.
Bring the milk to 195°F and stir often to avoid the milk from sticking to the bottom of the pot and scorching. The milk will be frothy and look like it is about to simmer when it is close to the correct temperature.
Once the milk reaches 195ºF, remove from the heat and add the vinegar all at once, stirring very slowly for 1 minute. You should see the curd begin to form and separate from the whey almost immediately. If the curd does not start forming right away, add another 2 tbsp of vinegar.
Move the pot to the sink and run a gentle stream of cold tap water into the curds, being careful not to lose any curds into the sink.
Once the curd reaches 115°F, pour the curds and whey into the cheesecloth lined colander and drain for 1 minute.
When most of the whey has drained off the curd, gather the corners of the cloth and loosely tie them together to form a bag.
Twist the cloth gently to wring out more whey, then open the cloth and flip the mass of cheese over.
Hang the cheesecloth bag from the neck of the sink faucet, or from the handle of a spoon hanging into a deep pot, to catch any additional whey that releases from the curd. Drain for 1 hour. For a firmer cheese, place the drained cheese in cloth between two dinner plates and place a 10 lb. weight on top of the plate and press for up to 2 hours.
Remove the cheese from the cloth and place in a bowl of cool water for 2 hours. This will draw out any additional vinegar, giving the cheese a sweeter taste.
Serve immediately or store the cheese in an airtight container in the fridge for up to 5 days.