1.Preheat oven to 200°C. Place four 2-cup (500ml) shallow ovenproof dishes on an oven tray.
2.Combine eggplant and salt in a colander over a bowl. Stand for 20 minutes.
3.Meanwhile, heat 1 tablespoon of oil in a large frying pan over medium heat. Cook onion, stirring, for 2 minutes or until lightly golden. Add mushrooms; cook, stirring, for 5 minutes or until browned lightly. Add garlic and tomato; simmer for 10 minutes.
4.Pat eggplant dry between sheets of paper towel to remove any excess moisture. Heat half of the remaining oil in a large clean frying pan over high heat; cook half the eggplant, stirring, for 3 minutes or until golden and tender. Repeat with remaining oil and eggplant. Stir eggplant and ¼ cup of the parsley into tomato mixture; season to taste. Spoon eggplant mixture into the dishes.
5.Combine egg yolks, whole eggs, yoghurt and 1⅓ cups of parmesan in a medium bowl. Spoon yoghurt mixture over eggplant mixture in dishes; smooth top. Sprinkle with remaining parmesan. Bake for 12 minutes or until golden. Serve topped with remaining parsley.
Eggplant and tomato mixture can be made a day ahead, to the end of step 4.
Traditionally parmesan is made with calf rennet. When purchasing check ingredients to see that the cheese is vegetarian, make sure it doesn’t contain calf rennet.