Meanwhile, preheat your oven to the broil setting and position a rack in the upper third of the oven. Arrange the eggplant slices in a single layer on two parchment-lined baking sheets. Using the remaining oil (but saving the last teaspoon), brush the eggplant with oil. Broil one sheet at a time until the eggplants are deeply golden and slightly charred, about 5 minutes. Flip, brush with oil again, and broil for another 3 minutes. Sprinkle with a pinch salt immediately after removing from the oven. Repeat with the second tray.