Heat oven to 300° F. Spray a rimmed baking sheet with the cooking spray.
Heat the oil in a large saucepan over medium heat. Add the popcorn kernels, cover, and cook, shaking the saucepan constantly once the kernels begin to pop, until there is a 2- to 3-second interval between pops, 5 to 7 minutes. Transfer to a large bowl.
In a medium saucepan, combine the butter, sugar, and corn syrup. Cook over medium heat, stirring frequently, until the mixture bubbles and lightens in color, 3 to 5 minutes. Stir in the vanilla and salt. Pour over the cooked popcorn and, with a rubber spatula, toss to coat.
Spread the popcorn mixture on the prepared baking sheet and bake, tossing once, until deep amber, 30 to 35 minutes. Remove from oven, toss, and let cool on the baking sheet. (The popcorn will crisp as it cools.)