Pour the milk into a large pot and heat over medium heat until it reaches 185°F (85°C). Maintain the temperature between 180–190°F for 10 minutes, stirring occasionally.
Remove from the heat and allow the milk to cool to 110°F (43°C) or below. It should feel warm but not hot to the touch.
Transfer the cooled milk to the Instant Pot insert.
In a small bowl, whisk together about 1 cup of the warm milk and the ¼ cup Greek yogurt until completely smooth. Pour the mixture back into the remaining milk and whisk well to combine.
Place the insert into the Instant Pot. Cover with the lid and select the Yogurt function. If your model allows temperature adjustment, set it to 109°F. Incubate for 9–12 hours, depending on how tangy you like your yogurt. The longer it cultures, the tangier it becomes.
Once the yogurt has set, cover the insert and place the entire pot in the refrigerator overnight to chill completely.
The next day, whisk the yogurt until smooth and creamy.
Pour half of the yogurt into a Greek yogurt strainer and place it in the refrigerator. Strain for at least 3 hours, or overnight for a thicker yogurt.
Transfer the strained yogurt to a storage container and repeat with the remaining half of the yogurt.
Store in the refrigerator for up to 2 weeks.