In a large saucepan on (a strong) medium, pour 7 cups of the milk and slowly heat it up until it starts to steam a little (probably about 10 minutes).  You don't want to overdo it and scald the milk, so be patient and don't turn the heat up too high. 

While the milk is heating, pour the remaining 1 cup of milk, the cornstarch, sugar, lemon zest, and fresh lemon juice into a blender and blend for 10 seconds.  If you really need it to be super lemony you can add a little lemon extract, but be careful because it can be a little overpowering and fake.

Once the milk is steaming, slowly pour the milk/cornstarch/lemon mixture in while stirring continuously.

Turn the heat down to medium-low and continue to stir as the mixture slowly thickens. This will take 10-15 minutes. The stirring is SUPER important because it's going to try to stick to the bottom and you need to keep scraping that off.

Once it's thickened, remove the pan from the heat and stir in the vanilla. Let it sit and cool a little before serving (or chilling, in my case...hot pudding is weird and gross).