Peel the outer layer of the broccoli stalks. Cut the broccoli lengthwise keeping the stalk and broccoli florets intact. (The long broccoli spears should resemble trees.) Arrange in a single layer on a baking sheet. Drizzle with olive oil and season with salt and pepper, to taste. Toss to coat and roast until nicely caramelized, about 15 minutes. Turn broccoli over and sprinkle with grated the Parmesan. Cook until the Parmesan melts, about 5 minutes. Transfer to a serving bowl or platter and serve immediately.