Season eggplant generously with salt, and toss in a colander set over the sink. Allow to sweat while you prepare the beef.
Combine the garlic, dark parts of the scallions, and ground beef in a medium mixing bowl, and season with salt. Mix well with your hands, and smush into a ball.
In a large skillet, heat the ghee over medium-high heat. Cook the meat until brown and starting to crisp, about 3 minutes. Transfer meat to a plate and set aside.
Gently squeeze the eggplant over the sink to remove any last drops of excess water, and add to the skillet. Cook until well-browned on all sides, but not mushy, 2-3 minutes.. Return the browned meat to the skillet and toss just to combine, killing the heat.
Spoon eggplant-meat mixture into bowls, and top with herbs. Squeeze lime juice over, and serve with lime wedges.