Cook pasta in boiling salted water. Cut off and discard woody ends of asparagus; cook spears in small amount of water in microwave until almost tender, about 3 minutes. Remove spears from water, reserving water, and cool under cold running water. Cut diagonally into 2-inch sections; set aside. In large frying pan, heat olive oil until hot. Add green onions and garlic; cook, stirring frequently, until onions are softened. Add shrimp and cook 1 to 2 minutes, stirring frequently, until shrimp begin to turn pink. Add asparagus and 1/4 cup of asparagus cooking water. Cook over high heat until shrimp are cooked and water has reduced by about half. Drain pasta and add to frying pan. Toss, adding butter, salt, pepper and Parmesan cheese to taste. Serve immediately.