How to Make It
Combine first 5 ingredients in a large bowl. Divide lamb mixture into 4 equal portions, shaping each into a 1/2-inch-thick patty. Place patties on a grill rack; grill 4 minutes on each side or until lamb is done. Keep warm.
Heat 1 teaspoon oil in a large nonstick skillet over medium-high heat. Add eggplant, and sauté for 3 minutes. Remove from pan. Heat 1 teaspoon oil in pan; add onion, and cook 7 minutes or until golden brown, stirring frequently. Add mushrooms; cook 3 minutes. Stir in eggplant and vinegar. Remove from heat.
Place 1 tomato slice and 1 patty on each roll half; top each with three-fourths of eggplant mixture.