Heat 1 tbsp oil in a large heavy pot over medium-high heat. Add the popcorn kernels, cover with a lid, and cook, shaking the pot occasionally, until popping slows to 2 to 3 seconds between pops.

Transfer popped corn to a large buttered mixing bowl. Pick out and discard any unpopped kernels.

Combine brown sugar, butter, corn syrup, milk, and salt in a 3-quart heavy-bottomed saucepan over medium heat. Stir until the butter melts and the sugar dissolves, about 3 minutes.

Clip a candy thermometer to the side of the pan. Increase heat to medium-high and cook without stirring until the caramel reaches 235 F (soft-ball stage), about 8 to 10 minutes. Watch it closely after 230 F.

Remove from heat immediately. Stir in vanilla extract and baking soda - the mixture will bubble briefly. Stir just until combined.

Pour the hot caramel over the popcorn in a thin, steady stream. Fold quickly with a buttered wooden spoon until all the popcorn is evenly coated.

Butter your hands well. Scoop roughly 1/2 cup of coated popcorn and press firmly into a round ball about 6 cm (2.5 inches) across. Work quickly before the caramel stiffens.

Set each finished ball on a sheet of wax paper. Repeat with remaining popcorn, re-buttering your hands between each ball.

Leave balls to cool completely at room temperature for 10 minutes before wrapping individually in wax paper.