Line 2 half-sheet pans with silpats, parchment paper or non-stick foil. Preheat oven to 250°F.
Combine brown sugar, butter, corn syrup, vanilla and salt in a heavy, medium-sized saucepan over medium high heat. Bring to a boil. Boil for 5 minutes, stirring occasionally. Remove the pan from the heat and add the baking soda. It will foam up big time! Don't worry, it's to be expected.
Pour the molten caramel over the popped corn in the bowl and stir gently but thoroughly to evenly coat the popcorn. Split the popcorn between the two prepared pans and spread it out evenly. Bake in the oven for 1 hour, stirring well every 15 minutes. Grandma says "Watch it closely during baking to ensure it doesn't stick and burn. If it tends to do this, lower the temp a tad. This step is what makes it crisp and it does not stick to your teeth!"
Let the caramel corn cool on the pan (if it is sufficiently done, you'll hear it crackling as it cools!), then store in an airtight container at room temperature.