Heat oven to 400° F. Using a fork, prick the eggplant all over. Place on a foil-lined baking sheet and roast until very tender, 50 to 60 minutes.
When the eggplant is cool enough to handle, halve it lengthwise and scrape out the flesh, discarding the skin. Finely chop the flesh and transfer it to a large bowl.
Add the onion, garlic, parsley, oil, vinegar, mayonnaise (if using), ½ teaspoon salt, and ¼ teaspoon pepper and mix to combine. Sprinkle with additional parsley and serve with the bread and vegetables, if desired.
