Spread popcorn in the bottom of a large, deep roasting pan. Sprinkle peanuts over the popcorn.
Combine brown sugar, butter, corn syrup, and salt together in a saucepan over medium-high heat. Cook, whisking constantly, until sugar and butter are melted and sauce is thick and caramelized, 2 to 3 minutes.
Pour caramel sauce over the popcorn and peanuts and stir to coat popcorn and peanuts completely, scooping any peanuts and caramel that fall to the bottom of the roasting pan.
Bake in the preheated oven, stirring occasionally, until caramel and popcorn are crisped, about 45 minutes. Turn popcorn out in a single layer on a sheet of parchment paper to cool completely.