Line a baking sheet with parchment paper and lightly butter or spray the parchment. Butter or lightly oil your hands so the warm caramel mixture will not stick while you shape the popcorn balls.

Place the 10 cups of freshly popped popcorn in a very large heatproof bowl. Remove every unpopped kernel, then add the optional peanuts, pretzels, or roasted nuts.

Melt the butter in a saucepan over medium heat. Add the brown sugar, light corn syrup, and salt, stirring until the sugar is moistened and the mixture begins to bubble.

Bring the caramel to a steady boil and cook for about 4–5 minutes, or until it reaches approximately 245–250°F (118–121°C) on a candy thermometer. Do not overcook, because caramel that goes beyond this range can become too hard.

Remove the saucepan from the heat and immediately stir in the vanilla extract and baking soda. The caramel will foam slightly as the baking soda lightens its texture.

Pour the hot caramel over the popcorn mixture right away. Stir carefully with a buttered spatula or wooden spoon until the popcorn and optional add-ins are evenly coated.

Let the coated popcorn cool for about 3–5 minutes, just until it is warm enough to handle. With buttered hands, firmly press the mixture into 10–12 balls about 3 inches wide.

Place the shaped popcorn balls on the prepared baking sheet and sprinkle each with a small pinch of flaky sea salt if desired. Let them cool completely before wrapping them individually in plastic wrap or parchment.