To pop your popcorn in a large pot: Put oil and a few popcorn kernels in a large pot- at least an 8 quart with a lid. (If you don't have a large enough stock pot, then just divide the oil and popcorn in half and pop it in two batches.) Heat on medium high. When kernels begin popping, add the rest of the popcorn kernels and replace lid. Shake gently using the handles of the pot. Popcorn will begin popping rapidly. (once you put all of the popcorn in the pot, it only takes a couple of minutes to be done.) Listen closely, when pops space out to a few seconds between each one, the popcorn is done- remove it from the heat. Keep the lid on as a few more pieces will pop. Transfer popcorn to a gigantic bowl or 2-3 smaller bowls. Remove any unpopped kernels.
To make the caramel sauce: Combine brown sugar, butter and corn syrup in a medium sized saucepan. Begin heating mixture on medium-high heat (I put mine at a 6.) Once it begins to boil, add in sweetened condensed milk and return to a boil. Once it begins to boil again, it will take about 10 minutes to get to soft-ball stage. If you have a candy thermometer, it will read between 235 degrees F and 240 degrees F. If you don't have a candy thermometer, set the timer after it begins boiling again (after you add the sweetened condensed milk) for 10 minutes. At that point, take a small amount of caramel and drop it in cold water. It should immediately form a small ball that can be squished flat if you press on it. If the caramel doesn't form the ball, cook it an additional minute and try again. You can read a bit more about the stages of candy making here.
Once caramel is at soft-ball stage, remove from heat and add in vanilla. Don't forget this step! Stir to combine.
Pour caramel over popcorn and stir with rubber scrapers to coat. That's it! You now have 32 cups of caramel popcorn. Now simply invite all your friends over and ENJOY!