Preheat your oven to 180 degrees.
Pour the goat milk into a pot and heat slowly on the stovetop on medium-low heat, stirring frequently.
Once it gets close to boiling and bubbles begin forming around the edges, place it in the oven for 30 minutes.
Turn off the oven, leaving the door ajar so it can cool.
If you are using yogurt as a starter, remove it from the fridge so it can come to room temperature.
Remove the hot goat milk from the oven, and let it cool without stirring until you can move your finger back and forth 10 times without getting burnt (it will still be pretty hot).
Once the milk has cooled enough, stir in the room-temperature yogurt starter.
Place the lid on the pot and wrap it in a large towel.
Put the pot in the oven and turn on the oven light.
Let the yogurt ferment undisturbed for approximately 8-12 hours.
Remove the goat yogurt from the oven.
There will likely be some liquid whey in the pot along with the goat yogurt, so whisk it into the yogurt until it's smooth.
Place the yogurt in an airtight container in the fridge. As it sits in the fridge it will continue to thicken slightly for the first number of hours.