Toast cumin in a dry 10-inch heavy skillet (preferably cast-iron) over medium heat, stirring occasionally, until fragrant and dark brown (be careful not to burn). Cool, then grind to a powder in grinder.
Pan-roast whole eggplant in skillet over medium heat, turning frequently with tongs, until blackened and tender, 20 to 30 minutes.
Transfer to a cutting board and cut off and discard stem. Scrape flesh from skin and coarsely chop. Toss with onion, vinegar, sugar, 1 tablespoon oil, 1 tablespoon parsley, 1/2 teaspoon toasted cumin, and 1/2 teaspoon salt.
Serve in a shallow bowl drizzled with remaining tablespoon oil and sprinkled with remaining tablespoon parsley and toasted cumin.