Pour the milk into a large saucepan and heat it over medium heat until it just starts to simmer. Do not let it boil.
Remove the milk from heat and let it cool to about 40°C (105°F). You should be able to comfortably touch the milk with your finger.
Stir in the plain yogurt or buttermilk. If using, add sugar and vanilla extract at this stage.
Cover the saucepan with a clean towel or cloth and let it sit undisturbed in a warm place for 6-12 hours, or until the milk has thickened and set into a curdled consistency. The time required will vary depending on the ambient temperature.
Once set, gently stir the lait caillé, cover it with a lid or plastic wrap, and refrigerate for at least 2 hours before serving.
Enjoy your meal!