In the bottom of a medium size baking dish or pie tin, layer the thinly sliced vegetables, adding the butter, garlic and cheese in between each layer.
Mix together the milk, cream and truffle oil in a jug and then carefully pour over the vegetables making sure it gets between all of the gaps and all of the vegetables are covered.
Combine the breadcrumbs, chopped cobnuts and parmesan then sprinkle over the dish.
Bake in the centre of the oven for 45 minutes or until the vegetables are all cooked and the top is crisp and golden.
Serve with truffle shavings and a sprinkling of thyme.