Heat a large rimmed skillet over medium heat. Once hot, add oil and the eggplant cut-side down and cover - you may have to do this in two (or more if increasing batch size) batches depending on the size of your pan. Cook on one side for 4-5 minutes or until slightly charred. Then flip the eggplant over on the other side, cover, and cook for 4-5 minutes more. You're looking for the eggplant to be softened and browned on the outside.