Drizzle basil infused oil over the popcorn. Grind grey salt in a spice grinder (a coffee grinder also works well for this purpose) until fine it will stick to the popcorn more evenly if the crystals are smaller. Add black pepper, then grate parmesan over the popcorn.
Preheat a large cast iron Dutch oven on a stovetop over high heat. Add olive oil, then popcorn. As soon as it begins to pop, cover and turn down to medium heat until sound of popping stops, about 3 to 4 minutes.