To make polenta base, preheat oven to 200°C. Grease a 35 x 12cm rectangular tart tin with removable base. Sprinkle a small amount of dry polenta over base and sides. Bring water to the boil in a large saucepan. Add polenta and salt and stir over a low heat for 5 minutes or until thick.
Stir in parmesan until melted. Spread in prepared tin and allow to set for 10 minutes. Bake for 15 minutes or until crisp on top. Remove and set aside whilst preparing vegetables.
To make vegetable top, heat oil in a medium non-stick frying pan over a medium to high heat. Add mushrooms, asparagus and garlic. Cook, stirring, for 5 minutes. Spread half of the tomatoes over polenta base. Top with mushrooms and asparagus, remaining tomatoes and sprinkle with feta. Return to oven for 10 minutes or until feta is lightly browned. Allow to stand for 10 minutes.
Meanwhile, combine basil and oil then season. Remove tart from tin and drizzle with basil oil. Cut into wedges to serve.