1. Bring 6 cups water and 1 teaspoon salt to a boil; add pasta, and boil 6 minutes or until almost tender.
2. While pasta cooks, combine 4 eggs and next 4 ingredients in a medium bowl; stir well with a whisk. Set aside.
3. Cut asparagus into 1 1/2-inch pieces. Place oil and butter in an ovenproof 10-inch nonstick skillet, and place over medium-high heat until butter melts. Add asparagus, and sauté 2 minutes. Remove asparagus from pan. Add mushrooms, onion, and garlic; sauté 3 minutes or until onion is tender and liquid evaporates. Remove pan from heat. Add asparagus. Drain pasta, and add to vegetables in pan. Stir in chopped basil and oregano.
4. Pour egg mixture over vegetables and pasta in pan. Place over medium heat. Cover and cook 8 minutes or until top is almost set (do not stir). Sprinkle with cheese.
5. Preheat broiler.
6. Broil 2 minutes or until golden. Cut into wedges. Serve with marinara.