In a saucepan, heat the whole milk over medium heat until it just begins to simmer. Do not let it boil. Remove from heat and let it cool to a temperature of about 110°F (43°C), or until it feels warm but not hot to the touch.
In a small bowl, mix the plain yogurt with a few tablespoons of the warm milk to thin it out and make it easier to incorporate.
Stir the thinned yogurt mixture back into the warm milk. If using, add sugar and vanilla extract, and stir to combine.
Pour the milk mixture into a clean, covered container. Place the container in a warm, draft-free area to maintain a consistent temperature. You can use a yogurt maker, an oven with the light on, or wrap the container in a towel and place it in a warm spot.
Allow the mixture to incubate for 6-12 hours, or until it has thickened to your desired consistency. The longer it sits, the tangier it will become.
Once the yogurt has set, transfer it to the refrigerator and chill for at least 2 hours before serving.
Enjoy your meal!