Arrange the oven racks in the upper and middle thirds of the oven. Preheat the oven to 275°F. Line two half-sheet pans with parchment paper.
Pop both bags of popcorn according to the package directions. Open the bags so the steam can escape.
Transfer the popcorn from one bag to a large bowl. Remove any unpopped kernels you come across. Have the parchment-lined sheet pans, rubber spatula, and a heatproof measuring cup ready before starting the caramel mixture.
Melt the butter in a medium saucepan over medium heat. Add the brown sugar, water, and vanilla extract. Stir well with a fork or whisk to combine.
Cook the mixture for 5 minutes, stirring frequently at first. Once it starts to simmer, lower the heat to medium-low to low and stir constantly. Do not leave the mixture unattended; it can boil over quickly.
At the end of 5 minutes, remove the pan from the heat. Continue stirring until it stops simmering. The mixture will be thin and pourable; it does not need to reach a specific candy temperature.
Carefully transfer the caramel mixture to a heatproof measuring cup. You should have about 1⅓ cups. This makes it easier to divide and pour over the popcorn.
Slowly pour a generous ⅔ cup of the caramel mixture over the popcorn in the bowl while gently folding and tossing with a rubber spatula. Continue folding until the popcorn is evenly coated, taking care not to crush or break it.
Transfer the coated popcorn to one prepared sheet pan and spread it out as close to a single layer as possible.
Transfer the second bag of popcorn to the bowl, removing any unpopped kernels you come across. Repeat the coating process with the remaining caramel mixture, then spread the popcorn on the second prepared sheet pan.
Bake for 1 hour, stirring the popcorn every 15 minutes with a rubber spatula. During the first two stirs, scrape up any caramel that has collected on the parchment and gently fold it back into the popcorn. Halfway through the baking time, rotate the pans from top to bottom and bottom to top.
After 1 hour, turn off the oven and crack the oven door open slightly. Leave the popcorn in the warm oven for 5–10 minutes. It should be dry and crisp. If the coating is still a little tacky, leave it in the warm oven for a few minutes longer.
Remove the pans from the oven. Gently stir the caramel popcorn once more to separate the pieces, then let it cool completely.