Preheat oven to 275°F. Line a baking sheet with parchment paper and set aside.
Heat oil in a large covered pot over medium-high heat. Add a couple of kernels with a pinch of salt. When the kernels pop, remove from heat and add the rest of the kernels and cover immediately. Count to 30 seconds, kernels should start popping. Crack the lid a bit to allow steam to escape.
Continue allowing kernels to pop, shaking pot periodically so the kernels don’t burn at the bottom of the pot. Once kernels stop popping, remove from heat and dump popcorn into a large bowl and set aside.
Remove any burnt pieces in the bottom of the pot as this pot will be used to make the sauce.
Pour Ginger Beer, rum and lime juice into the pot. Lower heat to medium and bring mixture to a boil. Reduce heat and simmer until mixture has reduced about two thirds.
Pour mixture into a bowl and set aside.In a pan, melt butter and add brown sugar. Stir to combine and allow mixture to melt and bubble slightly around the edges.
Continue stirring until color changes to an amber color and mixture starts to get thick and sticky. Add the ginger beer and rum mixture to the pan as well as the baking soda. Stir vigorously. Do not allow mixture to harden like candy.
Immediately pour over popcorn and mix using a spatula to evenly coat the popcorn. Spread popcorn onto the baking sheet in a single layer, sprinkle remaining sea salt and place inside oven.
Bake for 40-45 minutes, to dry the popcorn. Remove from oven and allow to cool. Break into clusters on sheet and sprinkle lime zest.