Trim the bottom ⅛ inch (3 mm) off the broccoli stalks and use a knife or a vegetable peeler to scrape the tough outer layer of the stalks. Cut the broccoli heads into rough spears—a small floret at the top, with as much of the long stalk as possible attached to each. (If you have time, and if you prefer softer broccoli, blanch it for 1 to 2 minutes in a pot of boiling water, drain in a colander, and cool under running water.) If doing this in the morning, put in a baking dish or bowl, cover, and refrigerate.
Drizzle the broccoli with the oil and rub it in well with your hands to thoroughly coat the spears. Sprinkle with the cheese, a couple of good pinches of salt, and a few grindings of pepper. Toss well. Spread the broccoli on the hot baking sheet in a single layer (it should be hot enough that the broccoli sizzles immediately), scraping any cheese and oil left in the baking dish over the spears.
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