Heat the oil and fry eggplant for several minutes until lightly browned and drain on kitchen paper; add onion, garlic and mushrooms to the pan and more oil if necessary. Cook until the onion is soft. Combine tomatoes, wine and stock with onion mixture and simmer for 15 minutes or until thick. Stir in eggplant.
Cook pasta until tender, drain. Combine pasta with half of the eggplant mixture. Spread into a large ovenproof dish. Whisk together ricotta, milk and eggs and spread half the mixture on top of pasta mixture. Top with half the cheddar cheese, then add remaining eggplant mixture and sprinkle with remaining cheddar and Parmesan. Bake at 350 degrees for 40 minutes.