Heat the oven to 200°F (93°C), then line 1 or 2 12×17-inch baking sheets with silicone baking mats or parchment paper. The lined pans prevent the caramel coating from sticking as it firms.
Place the popcorn in your largest bowl, or distribute it across the prepared baking sheets. Leave enough room to turn the popcorn gently without crushing the kernels.
Put the brown sugar, corn syrup, butter, salt, and cream of tartar in a medium saucepan over medium heat, stirring continuously until the butter has melted and the mixture begins simmering. Once bubbles appear around the edges, stop stirring and let the syrup boil for 4 minutes, reaching 234–235°F (112–113°C) on a candy thermometer if using one.
Take the saucepan off the heat and immediately stir in the baking soda. The caramel will rise, foam, and nearly double in volume, so stir carefully and keep hands away from the hot steam.
Pour the foamy caramel over the popcorn and fold with a large spoon or spatula until the kernels are coated, then spread the popcorn across the prepared pans. Work steadily but gently as the coating begins to thicken and cling to the popcorn.
Bake for 1 hour, using a gentle hand to stir the popcorn every 20 minutes. Each turn redistributes the glaze and helps moisture escape so the coating dries evenly.
Leave the caramel corn on the pans to cool for at least 30 minutes, then separate any large clusters once they are comfortable to handle. It may feel a little soft right out of the oven, but the coating hardens into a crisp shell as it cools.
Seal the completely cooled caramel corn tightly in an airtight container. Protected from humidity, it stays fresh for up to 2 weeks.