Trim off the large leaves of the broccoli; remove and discard tough ends of the lower stalks. Wash broccoli thoroughly. Cut the broccoli into flowerets; cut the upper stalks into 1/2 inch pieces.
Cook the broccoli in a small amount of boiling water for 10 to 12 minutes, or until crisp-tender; drain well. Set aside.
Start the water for the pasta. Saute the sliced green onions and garlic in 1 tablespoon melted butter in a skillet over medium heat until tender. Add the wine; reduce heat, and simmer uncovered, 5 minutes. Add the olive oil, 3 tablespoons melted butter, and broccoli; cook over medium heat until thoroughly heated.
When you see the pasta water is boiling, cook pasta according to package directions and drain well. Combine the cooked pasta and broccoli mixture in a large serving bowl, tossing gently to combine. Sprinkle with Parmesan cheese and serve immediately.