1.Preheat oven to 200°C. Grease deep 2.5-litre (10-cup) casserole dish.
2.Heat oil in large frying pan, cook onion, garlic, mushrooms, carrot and eggplant, stirring, until onion softens. Add mince, cook, stirring, until browned. Add flour, cook, stirring, 1 minute. Add wine, bring to the boil, stirring. Stir in undrained tomatoes, paste, sauce and oregano. Reduce heat, simmer, uncovered, 10 minutes or until mixture thickens slightly.
3.Meanwhile, make soft polenta. Bring stock and milk to the boil in large saucepan. Gradually add polenta to stock mixture, stirring constantly. Reduce heat, cook, stirring, about 10 minutes or until polenta thickens. Stir in cheese.
4.Boil, steam or microwave potato until tender, drain. Mash potatoes with butter and milk in large bowl until smooth. Using wooden spoon, gently swirl hot polenta mixture into potato mixture.
5.Spoon mince mixture into dish, top with potato polenta mixture, sprinkle with cheese. Cook in oven, uncovered, about 25 minutes or until cheese browns lightly.