Parboil broccoli in 1/2 cup water for 3 to 5 minutes. Drain. In medium skillet, sauté onion and garlic in vegetable oil or butter until tender but not brown. Add pepperoni and mushrooms and cook over medium heat 5 minutes more. Add broccoli and mix. Meanwhile, cook the spaghetti according to package directions. Drain. Toss spaghetti with other ingredients, including Parmesan cheese, and serve.