Heat vegetable oil in a large stock pot over medium heat for 2-3 minutes. Add popping corn and stir to coat the kernels with the oil. Cover with lid. Gently and carefully move the pan back-and-forth every 30 seconds or so to keep the kernels from sticking and burning. Kernels should begin to pop within a minute or two. Continue moving the pan intermittently until the popping has almost stopped. Turn off heat. When popping has stopped, pour popped corn into a large bowl.
While popcorn cools, place butter in a sauce pan and melt over low heat. Add brown sugar and corn syrup. Stir to combine. Turn heat up a little and stir frequently as it comes to a slow, low boil. DO NOT RUSH THIS STEP -- bringing the syrup to a boil too quickly results in sticky caramel corn. When a line of bubbles form along the edge of the pan, reduce the heat to low and start a timer set for 5 minutes.
Preheat oven to 250°.
While syrup is heating, transfer 14 cups of the popped corn to a heat-tolerant bowl. Unpopped kernels should stay at the bottom of the first bowl and not end up in your caramel corn.
Stir syrup slowly and almost constantly, scraping the bottom of the pan to avoid burning. A rubber spatula works great for this. Syrup will come to a rolling boil by the end of the 5 minutes.
When the time is up, remove pan from heat and stir in vanilla. Syrup will "fizz" in reaction to the vanilla. Make sure you enjoy the aroma as you stir!
Add the baking soda, stirring to distribute. This will cause the syrup to bubble up and thicken.
Pour immediately over the popped corn. Fold syrup into the corn to distribute.
Divide mixture between two rimmed cookie sheets or bar pans. I prefer using stoneware pans. Bake for one hour, stirring the caramel corn every 15 minutes.
Remove from oven. Spread out a couple sheets of aluminum foil on the countertop and transfer caramel corn onto foil. Gently break up any large clusters and allow to cool completely.
Store in resealable bags. Freeze for up to 3 months.