Heat the oil in a large lidded saucepan over medium-high heat. Place three kernels in the oil, cover, and wait to pop. Once the third kernel has popped, add the remaining kernels. Replace the lid and gently shake. As the kernels begin to pop, reduce the heat to medium and continue to shake and cook the popcorn until the popping slows noticeably. Remove from heat and allow to cool.
In another saucepot, combine the brown sugar, corn syrup, butter, and salt over medium heat. Cook until all ingredients are melted and the mixture is smooth. Add the baking soda and stir.
Pour the popped popcorn into a large mixing bowl, adding the peanuts on top. Carefully pour the caramel into the mixing bowl, over the popcorn and nuts, gently folding and stirring until coated.
Scrape the popcorn mixture onto a parchment-lined, rimmed baking sheet, sprayed with non-stick spray.
Bake in the oven for 15 minutes, stirring once, and the mixture is golden brown. Allow to cool before breaking apart and serving.