Combine milk, buttermilk, vinegar and 1/2 teaspoon salt in a medium pot over medium heat.
Bring the mixture to 180° F, using a temperature probe to track the temperature. As the mixture heats up, curds will start to develop. With a spoon, gently move them to the center of the pot to allow them to accumulate in one large cluster. Once the mixture has reached 180° F, turn the heat off and let the mixture sit for 20 minutes. I have found this to be an important step in developing flavor and maximizing the amount of curds yielded from the milk. Even longer is fine, but I don't recommend shorter.
Line a strainer with at least 4 layers of damp cheesecloth and place over a large bowl. This is how you'll strain excess whey from the cheese.
Transfer the curds to the cheesecloth by pouring the pot of whey and curds into the strainer, allowing the large bowl to contain all the whey.
The whey can be discarded or saved for another use. The biggest thing I've used it for is making bread.
Strain the curds for at least 4 hours, and preferably overnight. If you choose to strain the cheese overnight, wrap it in the cheesecloth and keep in the strainer over a bowl in the refrigerator.
Place the cheese in a bowl and add the lemon zest, pepper and ground fennel. Taste and adjust for seasoning. Add the remaining salt if needed. Enjoy!!