Heat the oil in a large heavy-bottom pot over medium heat until very hot and shimmering. Add the popcorn and immediately cover with a lid. Shake the pot constantly, holding the lid on with a heatproof holder, until the popping starts, about 1 minute. Reduce the heat to medium and continue to shake the pot until the popping slows to just a few per 5 seconds, 1 to 2 minutes more. Remove from the heat and let stand for another minute to allow any last kernels to pop.
Spray a very large bowl with nonstick cooking spray. Put the popcorn in the bowl and remove any unpopped kernels. Add the peanuts. Spray a rubber heatproof spatula with the cooking spray and place next to the bowl.
Combine the brown sugar, butter, corn syrup and salt in a medium saucepan and set over medium heat. Cook, stirring, until melted and the edges of the mixture begin to bubble. Clip a candy thermometer to the pan so the bottom of the thermometer is resting in the sugar syrup but not touching the bottom of the pan. Boil, stirring, until the thermometer registers 3150°C (the hard-crack stage), about 8 minutes.
Turn off the burner and add the vanilla. Stir briefly, about 5 seconds--being careful not to burn yourself as the mixture bubbles up.
Immediately pour the caramel evenly over the popcorn and quickly stir with the prepared rubber spatula until the pieces are mostly separated, about 3 minutes. Pull apart any larger clumps, being careful because the caramel will still be hot in spots. Stir in the apple chips.
Cook's Note: Lightly spraying the measuring cup with cooking spray before measuring helps prevent the corn syrup from sticking.