Preheat the oven to 425 degrees F.
Cut the broccoli florets from the thick stalks, leaving an inch or two of stalk attached to the florets, discarding the rest of the stalks. 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 a sheet pan large enough to hold them in a single layer. Toss the garlic on the broccoli and drizzle with 5 tablespoons olive oil. Sprinkle with the salt and pepper. Roast for 20 to 25 minutes, until crisp-tender and the tips of some of the florets are browned.
Meanwhile prepare all the remaining ingredients, measured out and set aside ready to toss in quickly when the broccoli comes out of the oven. (You'll need to move quickly!)
Remove the broccoli from the oven and immediately toss with 1 1/2 tablespoons olive oil, the lemon zest, lemon juice, pine nuts, Parmesan, and basil. Serve hot.