Preheat your oven to 250°F (120°C). Line two large rimmed baking sheets with parchment paper. Pour the entire bag of puff corn into a large roasting pan and set aside.
Make the caramel: In a heavy-bottomed saucepan over medium heat, melt the butter. Add the brown sugar, corn syrup, sweetened condensed milk, and salt. Stir constantly with a silicone spatula, scraping the bottom and corners.
Boil to the right temperature: Bring the mixture to a gentle rolling boil. Continue boiling for 4 to 5 minutes, stirring constantly, until it reaches 270°F to 290°F (soft-crack stage) on a candy thermometer. The caramel should be deep amber and slightly thickened.
Add vanilla and baking soda: Remove the saucepan from heat immediately. Stir in the vanilla extract, then add the baking soda. Stir vigorously until the caramel foams up and doubles in volume. This takes about 10 to 15 seconds.
Coat the puff corn: Slowly drizzle about one-third of the hot, foamy caramel over the puff corn. Gently fold with a spatula. Repeat with the remaining caramel in two more additions, folding gently each time. Try not to crush the puff corn.
Transfer to baking sheets: Spread the coated puff corn evenly onto the two prepared baking sheets. Break up any massive clumps, but leave small clusters intact.
Bake low and slow: Place both baking sheets in the preheated oven. Bake for 45 minutes to 1 hour, stirring every 15 minutes with a spatula to ensure even drying. The caramel will transform from sticky to dry and glossy.
Cool completely: Remove the baking sheets from the oven and place them on wire cooling racks. Do not disturb the caramel puff corn for at least 30 to 45 minutes. It will harden as it cools. You will know it is ready when the pieces make a clinking sound when tapped.
Break and store: Once fully cooled, break apart any remaining large clusters with your hands. Transfer to an airtight container lined with a paper towel. Store at room temperature in a cool, dry place for up to two weeks.
