Preheat oven to 200° F. Divide the popped popcorn between 2 large bowls, removing any unpopped kernels. Line two rimmed baking sheets with parchment paper, and set aside.
In a large deep saucepan, combine the brown sugar, corn syrup, butter, salt, and cream of tartar. Insert a candy thermometer. Bring to a boil, and cook the mixture over medium heat for about 5 minutes, stirring occasionally, until the thermometer registers 260° F (hard ball stage). Remove from heat, and quickly stir in the baking soda. The mixture will foam up quite a bit.
Pour the syrup mixture over the popcorn, half into each bowl. Work quickly to coat all the popcorn with the caramel. Spread popcorn evenly on the baking sheets, and bake for 1 hour, stirring and rotating the trays 3 times. Remove from the oven and spread popcorn on parchment paper to cool, breaking up the larger pieces if necessary.
This caramel corn stays fresh for up to 2 weeks in an airtight container on the counter.