In a skillet cook the potatoes in hot oil, uncovered, until tender. Add scallions, red pepper, mushrooms, and garlic. Cook until onion is tender. Then add the broccoli and cauliflower; reduce heat. Cook, uncovered, for approximately 5 minutes more.
Beat together eggs, cheese, wine, basil, salt, and pepper. Pour mixture over the vegetables in skillet. Cook over medium/low heat for 5 minutes. (If temperature is too hot, the egg mixture will overcook and become tough.) As eggs set, lift egg mixture around the edges with a spatula to allow the uncooked portion to flow underneath. Continue process until the mixture is almost set. The top will be moist.
Remove from heat. Cover and let stand until the top is set. Sprinkle with parmesan cheese. Cut, serve and enjoy!