Season both sides of the eggplant with salt and pepper. Let sit for 2 minutes. Heat 1/4 cup of the olive oil in a large skillet over medium-high heat. Pan-fry the eggplant slices, in batches, until golden brown on each side, about 2 to 3 minutes per side, adding more oil if necessary. Remove and drain on paper towels. Repeat the process with the remaining oil and eggplant.

Preheat a grill or panini press to medium high or heat a grill pan over medium high heat. Brush the grates with oil.

Lightly brush both sides of the bread with the extra- virgin olive oil. Place 3 slices of the eggplant over half of the bread slices. Lay a couple slices of cheese over the eggplant. Top the cheese with some of the peppers. Brush one side of the remaining slices of bread lightly with balsamic vinegar, then top the sandwiches with these slices of bread (balsamic coated sides facing in). Place the sandwiches on the grill (or in a panini press or on a grill pan) and cook until the cheese melts and nice hash marks form on crispy bread, 2 to 3 minutes per side. Serve warm.