Preheat a barbecue grill on medium. Spray both sides of the eggplant with oil. Cook one-third of the eggplant for 3 minutes each side or until tender and golden. Repeat, in 2 more batches, with remaining eggplant.
Step 2 Heat the oil in a medium saucepan over medium-low heat. Cook the onion, carrot, celery and garlic, stirring often, for 5 minutes or until soft. Add the tomato and bring to the boil. Reduce heat to medium-low. Cook for 20 minutes. Stir in the anchovy. Season with salt and pepper.
Step 3 Preheat oven to 200°C. Spray a 1.5-2L (6-8 cup) capacity baking dish with oil. Arrange one-third of eggplant over the base. Top with one-third of the tomato mixture and one-third of the parmesan. Continue layering with remaining eggplant, tomato mixture and parmesan. Sprinkle with breadcrumbs. Spray with oil. Bake for 25 minutes or until golden.