Separate the broccoli florets and trim the tough skin from the stalks. Put the broccoli leaves in boiling water with salt. A minute later, add the flowerettes. Return to a boil and cook for 6 to 8 minutes until tender but resistant to the bite. Drain.
Heat the olive oil in a pan and add garlic. Cook over moderate heat for a minute and add the broccoli leaves and flowerettes. Cook, tossing, for about 2 minutes. Correct seasoning and sprinkle with parmesan cheese to taste.