Wash the eggplants under running water and remove some of the peel but not all of it. Peel off one strip and then leave a strip of peel on and then peel off a strip next to it until you go all the way around the eggplant. In this way, you will remove the natural bitterness of the vegetable without compromising the shape.
Cut the eggplants crosswise into 1-inch thick disks.
Turn on the grill and cook the slices on low heat for 10 minutes on each side, or until they are completely cooked through. They should be quite firm on the outside but very soft in the middle.
Meanwhile, prepare the dressing. Slice the garlic as thin as possible and finely chop the mint leaves. Put them into a small bowl and add extra virgin olive oil, and white wine vinegar. Whisk everything together with a fork for a few seconds. Salt and pepper, to taste.
When the eggplants are ready, transfer them on a serving platter and cover evenly with the dressing.