In a large bowl, coat eggplant with olive oil and balsamic vinegar. Season with salt and pepper.
Arrange half of the eggplant slices on a tray. Place a slice of tomato and a slice of goats cheese on each slice of eggplant. Sprinkle a little salt and pepper on the tomatoes and cheese. Top with remaining slices of eggplant and secure each bundle with a toothpick.
Lightly oil the barbecue grate. Remove toothpicks and arrange bundles on grate. Cook about 7 to 8 minutes, then carefully flip. Continue cooking for 6 to 7 minutes.
To cook in the oven, bake at 190 degrees C for 15 to 20 minutes or until softened and delicious!
Fresh mozzarella can easily be substituted if you don't like goats cheese.