Stuffed Eggplant au Gratin

2 medium eggplants cut in half ( not length wise)
1/2 lb ground beef
1 chopped medium onion
2 garlic cloves minced
1/2 teaspoon salt
1 tablespoon lime juice
freshly ground pepper
1 teaspoon thyme
1/2 Lb can tomatoes, crushed and drained
1/4 cup chopped olives ( green or black)
1/4 cup grated Parmesan cheese to sprinkle

Boil eggplants in salted water for about 10 minutes, until partially softened.
Let them cool down slightly then remove the flesh gently.
In large skillet brown ground beef in a tablespoon vegetable oil. Add chopped onion and minced garlic and cook until tender. Add remaining ingredients except for cheese.
Cook until most of the liquid evaporates.
Spoon mixture into eggplant halves and place them upright in oven-proof casserole.
Sprinkle with cheese.
Bake in preheated oven for 10 minutes and broil another 2 minutes until cheese starts to brown.