In a medium saucepan over medium heat, melt the butter. Add the brown sugar, corn syrup, and salt and whisk until mostly combined. Bring this mixture to a boil without stirring and allow it to continue boiling for 5 minutes. Remove the caramel from heat and add the baking soda, spices, and vanilla extract. Be careful, it may spatter. Add the pumpkin puree and whisk until combined. Pour half the caramel mixture over the popcorn (and peanuts if using), and stir with a rubber spatula several times. Pour remaining half of caramel and stir until evenly coated.
Spread the caramel corn onto your prepared cookie sheets and bake in the oven for about 40-50 minutes, stirring every 10 minutes or so with a pair of tongs.
Note: Your popcorn may be ready before the 40 minutes are up. At the 30 minute mark, test by removing a couple of caramel corn kernels, allowing them to come to room temperature. If they’re completely crispy, they’re ready; however, if they are mushy or have a bite to them, bake for 5-8 more minutes. Continue checking this way until your caramel corn has a crisp bite to it.
Remove baking sheets and place in a wire rack to cool completely before breaking apart.