Pop the popcorn: heat oil in a large heavy-bottomed pot, add kernels, cover and shake until popping slows; transfer to a large bowl, discarding unpopped kernels.
Preheat oven to 250°F (120°C) and line a baking sheet with parchment.
In a medium saucepan combine sugar, butter, and corn syrup over medium heat.
Stir constantly until butter melts and sugar dissolves, then bring mixture to a boil.
Cook without stirring until mixture reaches 240–245°F (115–118°C) on a candy thermometer (soft–hard ball stage).
Remove from heat and quickly stir in baking soda and vanilla — the caramel will foam and lighten.
Immediately pour the hot caramel over the popped popcorn in the large bowl.
Gently toss with a spatula to coat the popcorn evenly, working quickly before the caramel sets.
Spread the coated popcorn onto the prepared baking sheet in an even layer.
Bake for 30–40 minutes at 250°F (120°C), stirring every 10 minutes to dry and evenly coat the popcorn.
Remove from oven, let cool completely, break into clusters and sprinkle flaky salt if desired before serving or storing.