To a large, heavy-bottomed pot, add the milk. Warm it over medium-low heat, stirring occasionally so it doesn't scald on the bottom, until it reaches 190˚F. This can take up to 20 minutes, so don't rush it with high heat.
Turn off the heat. Pour in the vinegar and stir gently for just a few seconds, only enough to distribute it. The milk will start to separate almost right away. Let it sit, without stirring, for about 20 minutes, until the curds have separated and the whey is mostly clear.
Line a fine mesh strainer with a layer of cheesecloth and set it over a large bowl. Using a slotted spoon, gently lift the curds out of the whey and into the cheesecloth. Drain for about 30 minutes.
Gather the corners of the cheesecloth so the curds are fully enclosed, then run the bundle under cold water for about a minute, turning it gently, to rinse off the last of the whey. Set it back over the bowl and let it drain for about 10 minutes, until it stops dripping.
Transfer the curds to a bowl and break up any large clumps with a fork or your hands. Stir in the salt and heavy cream, then taste and add more of either until it's as creamy and salty as you like it.
Serve right away, or store in an airtight container in the refrigerator for up to 5 days. You can stir in more heavy cream or milk if needed before serving.
