Prepare a medium-hot fire in a charcoal grill with a cover, or preheat a gas grill to medium-high.
In a large bowl, combine the lamb, mint, pepper and salt. Mix gently but thoroughly, being careful not to overwork the mixture. Form the mixture into 6 patties. Set aside to let rest.
Toss the cheese slices and eggplant halves in 2 tablespoons of the olive oil and 1 tablespoon of the salt. Place on the grill rack and cook the cheese for 30 seconds; remove from the heat and keep warm. Cook the eggplant for 3 minutes per side. Remove from the heat and dice into half-inch pieces.
In a small bowl, combine the diced eggplant, remaining 2 teaspoons sea salt, tomatoes, lemon zest and juice, garlic, and parsley. Cover and set aside.
Brush the grill rack with vegetable oil. Place the patties on the rack over direct heat. Cook for a total of 4-5 minutes per side. A few minutes before the patties are cooked to your desired doneness, brush the inside of the rolls with the remaining 3 tablespoons olive oil and put on the grill to toast slightly.
When everything is ready, assemble the burgers - place a patty on each roll topped with a slice of grilled haloumi and a pile of eggplant salsa. Finish with top of roll. Enjoy!
Makes 6 burgers
Mary Beth Harris-Murphree, Tyler, Texas