To cook the eggplant on a gas grill, see the NOTE, below.
The dish can be refrigerated for up to 2 days; let it come to room temperature before serving.
4 to 6 servings.
3 to 6 tablespoons extra-virgin olive oil
1 large (1 3/4 pounds) eggplant (unpeeled), cut into 3/4-inch-thick rounds
1/4 cup finely chopped red onion (from 1/4 medium red onion)
1/4 cup capers, drained (see VARIATION, below)
1/4 teaspoon kosher salt, plus more as needed
1/4 teaspoon freshly ground black pepper
1 handful small fresh mint leaves, whole or chopped, for garnish
Position an oven rack 4 to 6 inches from the broiler; preheat to broil.
Line a rimmed baking sheet with aluminum foil, or have a broiler pan at hand.
Use a few tablespoons of the oil (to taste) to brush both sides of each eggplant slice, arranging them in a single layer on the pan or baking sheet as you work.
Broil for 5 minutes, or until the slices are browned. Use tongs or a fork to turn over the eggplant slices and broil them for about 5 minutes on the second sides.
Let cool for 3 minutes, then transfer to a serving platter.
Combine the chopped red onion, capers and the remaining tablespoons of oil (again, to taste) in a medium bowl.
Season with salt and pepper, then stir to incorporate. Scatter the red onion mixture over the eggplant slices. Sprinkle lightly with kosher salt, then scatter the mint over the top.
Serve at room temperature.
Instead of a final sprinkling of kosher salt, you could add 1 tablespoon of caper brine to the dressing.
To grill the eggplant, preheat a gas grill to 400 degrees. Brush the eggplant slices with oil on both sides; close the lid and grill for a few minutes on the first side, then turn them over, close the lid and grill until fork-tender.