Preheat your oven's broiler to high and place an oven rack in the highest position. Line a large baking sheet with aluminum foil and spray with cooking spray. Set aside.
Preheat a griddle or panini press on high.
Slice eggplant into ½" thick disks, discarding the ends. Brush each side of the eggplant lightly with olive oil and place on the prepared baking sheet. Broil until lightly browned and tender when pierced with a fork, about 5 minutes per side.
On a clean work surface, lay out the four bottom pieces of ciabatta. Spread 1 tablespoon of pesto onto each sandwich. Top with a slice of cheese, followed by tomato, eggplant, and another slice of cheese. Cover with the top half of the bread. Brush both sides of the sandwich with olive oil. Cook sandwiches in the panini press until crisp and melty, about 8 minutes. Slice in half and serve with giardiniera, chips, or fruit.