Preheat the oven to 175 degrees F (80 degrees C). Turn off oven when temperature is reached.
Combine water and milk powder in a saucepan over medium heat. Cook until an instant-read thermometer inserted into the mixture reads 115 degrees F (46 degrees C), 5 to 7 minutes.
Stir plain yogurt into the milk-water mixture. Add sugar and vanilla extract. Pour mixture into 2 clean, oven-proof containers. Place in the preheated oven until tart and as thick as heavy cream, about 8 hours. Reheat oven to 175 degrees F (80 degrees C) every 1 to 2 hours, or as needed, to keep yogurt at a temperature of about 115 degrees F (46 degrees C).
Cover yogurt and refrigerate until cooled and thickened to desired consistency, 1 to 3 hours.