Preheat oven to 400 degrees F (200 degrees C). Place eggplant on a baking sheet lined with aluminum foil; prick all over with a fork.
Roast eggplant in the preheated oven until very tender, 50 to 60 minutes. Let cool until easily handled, about 10 minutes.
Halve eggplant lengthwise and scrape out the flesh; discard skin. Chop flesh finely and transfer to a large bowl. Add onion, 2 tablespoons parsley, olive oil, mayonnaise, red wine vinegar, garlic, salt, and pepper; mix to combine. Garnish with remaining 1 tablespoon parsley.