Combine chopped tomatoes and onions with a big pinch or two of salt, a big pinch of pepper, ¼ cup olive oil, basil, oregano and balsamic vinegar. Let marinate for a few minutes to meld the flavors. Meanwhile, prepare the eggplant.
Cut ends off eggplants and slice ½ inch thick. Heat a grill pan over high heat until hot or heat grill until hot. Brush with olive oil and season with salt and pepper on both sides. Grill eggplant slices about 4 or 5 minutes until you get nice grill marks and the slices are golden brown. Turn over and cook until eggplant is softened and cooked through until about 3 or 4 minutes.
Just before serving, crumble the goat cheese into the tomato mixture and mix gently to combine. With a large slotted spoon, top each grilled eggplant slice with a spoonful of the tomato goat cheese mixture.