Preheat the oven to 375 degrees F.
Wash broccoli and dry well. Cut the broccoli florets from the thick stalks, leaving an inch or two of stalk attached to the florets. Set aside the rest of the stalks for another use, such as broccoli slaw. Cut the larger pieces through the base of the head with a small knife, pulling the florets apart. You should have about 8 cups of florets.
Place the broccoli florets on 1-2 sheet pan(s) large enough to hold them in a single layer. Drizzle with 4 tablespoons olive oil and sprinkle with the salt and pepper.
Put thinly-sliced garlic in a separate bowl and moisten with a slight amount of oil.
Roast broccoli 15 minutes. Then add garlic.
Roast for another 10 minutes or so, until the broccoli is crisp-tender and the tips of some of the florets are browned.
Remove the broccoli from the oven and immediately toss in a bowl with the lemon zest, lemon juice, and Parmesan cheese. Serve hot.