Preheat the oven to 325°F.
Brush a parchment paper-lined baking pan with a little olive oil or butter; set aside.
Pour the balsamic vinegar in a small saucepan; bring to a boil and let simmer (do this slowly, if you rush, it becomes bitter) until it reduces by half. Allow the syrup to cool to room temperature.
In a non-stick sauce pan, melt the sugar without any water over high heat. It's important to carefully watch the sugar. As soon as the edges of the pan start caramelizing, immediately lower the heat to medium-low.
Gently jiggle the saucepan in circles. Do not use a spoon! Lower the heat to the lowest setting when there are only a few remaining non-caramelized pieces. Don't let the sugar get dark brown or you'll get a burnt taste, which would be unpleasant.
When all the sugar is an amber color, remove from the heat, pause for about a minute (be careful of splattering when the oil is added), then slowly add the olive oil and salt. Stir frequently with a wooden spoon. Bring back to the stove using the lowest setting and add the corn syrup and the balsamic reduction. Turn off the heat, then add the baking soda (it will become foamy) and vanilla extract. Stir well.
Immediately pour the caramel while it's still hot over the pop corn in large bowl. Sprinkle the peanuts (if using) and mix the ingredients until the caramel sauce is spread uniformly.
Spread the pop corn onto the baking pan. Sprinkle with a pinch of salt so it enhances the taste of the popcorn.
Bake for 10 to 15 minutes. Check the pop corn frequently, stirring to cook evenly.
Remove from the oven and let cool for 15 minutes before serving.