Trim and discard eggplant stems. Cut each eggplant lengthwise into 1/4-inch-thick slices. Brush slices on each side lightly with olive oil.
Lay eggplant on a barbecue grill over a solid bed of hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds); close lid on gas grill. Cook, turning as needed, until eggplant is browned on both sides and soft when pressed, 6 to 8 minutes. Sprinkle lightly with salt and pepper; transfer to a platter.
In a 10- to 12-inch frying pan over medium heat, cook bacon until browned and crisp, about 8 minutes, turning slices as needed. Drain bacon on towels and discard fat in pan.
Cut baguette in half lengthwise. Spread pesto onto cut sides of baguette. Lay eggplant slices on bottom half of baguette and cover with bacon, tomatoes, cheese, and arugula. Set top half of baguette in place and, pressing sandwich firmly together, cut into 4 equal portions with a serrated knife. Add salt and pepper to taste.