Preheat the oven to 200 degrees F. Line a large baking sheet with parchment paper.
Add the popcorn kernels and oil to a large pot and turn the heat on to medium. As soon as the first kernel pops, top with a lid and continue to cook until the popping subsides, 3 to 5 minutes. Immediately remove from the heat and transfer to a large bowl. This will yield 5 cups popped corn.
In a large saucepan, add the brown sugar, butter and corn syrup and cook on medium heat until the sugar has dissolved, about 5 minutes. Remove from the heat and add the vanilla and baking soda. Pour the mixture over the popcorn in the bowl and stir everything together.
Tumble the mixture onto the prepared baking sheet and spread in a thin layer. Bake until the caramel has coated the popcorn nicely, giving it a stir every 20 minutes, about 1 hour.
After it comes out of the oven, sprinkle the sea salt evenly over the top. Give it one last gentle stir and allow it to cool to room temperature before breaking it apart into smaller pieces.