Put the milk, brown sugar (if you like it sweet), and the slit vanilla bean into a pot. Bring the mixture to a boil.
Remove the pot from the heat and strain the milk to remove the vanilla bean and any skin. Let the milk cool to about 50°C. You can use a thermometer or put a finger in: if you can hold it for about 5 seconds without burning yourself, the temperature is right.
Add 3 tablespoons of the cooled milk to the plain yogurt in a separate bowl and stir until smooth and no lumps remain. This tempers the yogurt.
Carefully pour the tempered yogurt-milk mixture into the remaining cooled milk and stir everything well.