Melt butter into oil, swirl to mix and add onions. Saute until light golden and add mushrooms. Cook another 2 minutes and remove from heat. Heat oven to 375F. Butter a large deep casserole dish. Wash vegetables (any combination of those mentioned or whatever you have on hand.) Slice all vegetables into thin slices, the length of each vegetable. Lay one layer of carrot and zucchini, sprinkle with half of the onions and mushrooms, one-third of the grated cheese, and salt and pepper, lay down a layer of broccoli and cauliflower, sprinkle with remaining onions and mushrooms, one-third of the grated cheese and salt and pepper. Lay down a layer of potatoes and sprinlde with salt and pepper. Dot with butter. Mix together milk and eggs and pour over mixture. Cover with foil and bake for 30 minutes. Uncover and bake for 15 minutes. Sprinkle with remaining one-third of the cheese, breadcrumbs and Parmesan mixture and bake another 15 minutes. Recipe by Mangia