Lay the eggplant slices in a single layer on 2 baking sheets and sprinkle both sides with salt. Set aside about 30 minutes, or until moisture beads on top of the eggplant.
Prepare a grill for medium-high heat. Rinse the eggplant to remove the excess salt and pat dry. Brush the eggplant slices with 3 tablespoons of the olive oil, coating both sides. Season with salt and pepper. Working in batches, grill the eggplant about 5 minutes per side, or until char marks form and the eggplant is very tender. Transfer to a platter as you finish each batch.
Meanwhile, grate the zest of the lemon into a small bowl. Halve the lemon and squeeze 2 tablespoons of juice into the bowl. Whisk in the vinegar, shallots, chopped mint and the remaining 5 tablespoons oil. Season the vinaigrette to taste with salt and pepper.
Spoon the vinaigrette over the grilled eggplant and sprinkle with the mint leaves. Using a vegetable peeler, shave thin slices of feta cheese over the eggplant. Sprinkle with pepper and serve.
Photograph by Ray Kachatorian
Courtesy of Food Network Magazine