Heat the oil in a heavy bottomed 3-quart pot over medium heat. (I used one that was 8 inches in diameter and 5 inches deep.) Add 3 kernels of popcorn to the pot and cover with a lid. This is how my mom did it. Don't ask me why it was 3 kernels and not 2 or 4. When the kernels pop (this usually takes about 2 1/2 - 3 minutes), add the 1/2 cup of popcorn in an even layer and cover with the lid, but not all the way. Leave it open about 1/2 inch to allow steam to escape but not wide enough to let the popcorn pop right out.
Shake the pot every now and then. If you can't shake it with the lid ajar, cover the pot, shake and open the lid again when you return the pot to the heat.
Once the popping reduces to several seconds in between each pop, take the pot off the heat and remove the lid. Sprinkle with sea salt and transfer to a serving bowl. Taste for salt and add another sprinkle if necessary. If you like melted butter on top, now's the time to drizzle it.