Preheat a grill to medium. In a large bowl, toss the eggplant slices with 2 tablespoons olive oil; season with salt and pepper. Grill, turning once, until softened, about 4 minutes.
Lay the bread on a work surface. Top 4 slices with a layer each of cheese, prosciutto, eggplant and another layer of prosciutto and cheese. Top with the remaining bread slices.
Brush the outside of the sandwiches with the remaining 2 tablespoons olive oil. Grill, covered, turning once, until crisp, about 2 minutes.