1. Using a sharp knife, slice the eggplant into 1/8-inch slices. Sprinkle with salt and place in a colander to drain 30 minutes. Rinse well and pat dry with paper towels.
2. Preheat oven to 400 degrees F. (200 degrees C.).
3. Halve tomatoes. Heat oil in a frying pan and fry the eggplant slices in batches until golden brown. Drain on paper towels.
4. Arrange the tomato halves and eggplant slices in a shallow ovenproof dish. Season with salt and pepper and sprinkle with Parmesan cheese. Bake 10 to 15 minutes until browned. Cool slightly and serve warm.