Pour the 4 cups of whole milk and 1/2 cup of heavy cream into a medium, heavy-bottomed saucepan. Heat over medium heat, stirring occasionally, until the mixture reaches 120°F on an instant-read thermometer; this should feel quite warm but not scalding to the touch.
Remove the saucepan from the heat and gently stir in the 1/3 cup of distilled white vinegar. The milk will immediately begin to separate into white, fluffy curds and a thin, yellowish liquid (whey).
Let the pot stand undisturbed for 30 minutes to allow the separation to complete. The curds will look like large, soft clumps floating in clear whey.
Line a fine-mesh strainer or colander with a double layer of cheesecloth. Carefully pour the curds and whey into the lined strainer set over a bowl to catch the liquid.
Gather the edges of the cheesecloth and gently squeeze the bundle to release excess whey. Be careful not to press too hard, as you want to keep the curds soft and moist.
Transfer the strained curds to a medium bowl and break them apart with a fork. Sprinkle the 1/2 teaspoon of fine sea salt over the curds and stir gently to combine. The final texture should be moist, creamy, and slightly lumpy.
Notes
Be careful not to press the curds too hard when straining to keep them soft and moist.