Preheat the oven to 250 degrees F (120 degrees C).

Spread popcorn in bottom of a large, deep roasting pan; sprinkle peanuts evenly over the top.

Combine brown sugar, butter, corn syrup, and salt in a saucepan over medium-high heat. Cook, whisking constantly, until sugar and butter are melted and the mixture is smooth and bubbling, about 2 to 3 minutes.

Pour caramel sauce over popcorn and peanuts; stir until completely coated, scooping any peanuts and caramel that fall to the bottom of the roasting pan.

Bake in the preheated oven, stirring occasionally, until the caramel coating is dry and crisp and popcorn is evenly coated, about 45 minutes. Transfer popcorn mixture to a sheet of parchment paper in a single layer to cool completely and harden.