Preheat the oven to 200°F (93°C). Position a rack in the center of the oven and line two large baking sheets with parchment paper or silicone baking mats.
Place 15 cups popped corn and 2 cups salted red skinned peanuts in a very large bowl (use two bowls if needed). Gently toss to combine and remove any unpopped kernels.
In a medium saucepan combine 1 1/2 cups packed brown sugar, 6 tablespoons light corn syrup, and 3/4 cup butter. Cook over medium heat, stirring constantly, until the mixture comes to a full boil.
Once boiling, reduce heat slightly to maintain a gentle, steady boil and continue to boil for 5 minutes, stirring frequently to prevent scorching.
Remove the saucepan from the heat and immediately stir in 1 teaspoon vanilla extract and 3/4 teaspoons baking soda. Stir quickly—the mixture will foam and lighten in color.
Pour the hot caramel evenly over the popped corn and peanuts. Using a large heatproof spatula or wooden spoon, stir thoroughly and quickly until the popcorn and peanuts are evenly coated.
Divide the coated mixture between the two prepared baking sheets and spread into an even single layer.
Bake on the center rack at 200°F for 1 hour, stirring and scraping the mixture from the edges every 15 minutes and rotating the sheets between racks or front-to-back for even baking.
Remove the baking sheets from the oven and let the popcorn cool completely on the sheets (it will crisp as it cools). Once cooled, break into clusters and store in airtight containers.