Preheat the grill. In a mixing bowl, toss the eggplant and carrots with olive oil. Season with salt and pepper. Grill the vegetables in batches for about 1 minute on each side. Remove from the grill. On a platter, arrange the grilled eggplant, carrots, and peppers on one side. Drizzle with the olive oil and balsamic vinegar.
Place each fillet between two sheets of plastic wrap. Using a meat mallet, pound the meat very thinly. Place the meat on the second platter. Season with salt and pepper. Drizzle the meat with the aioli. Mound the arugula in the center of carpaccio.
Core and slice the tomatoes 1/2-inch thick. Season both sides with salt and pepper. Place half of the tomatoes around the third platter. Slice the cheese into 1/2-inch slices. Season both sides with salt and pepper. Place the cheese on top of the tomatoes, around the platter. Top the cheese with the remaining tomatoes. Place the basil leaves on top of the tomatoes. Drizzle the entire platter with the olive oil.
Arrange the slices of prosciutto over the fourth platter. Using a sharp knife, make a criss-cross cut through the core of each fig. Arrange the figs around the prosciutto. Place the chunks of cheese in a small bowl. Also place the olives in a small bowl. Serve all of the platters and bowls with crusty bread.