Preheat oven to 425°F Wash the broccoli and dry it THOROUGHLY. (If it's still damp, it will not brown properly.).
Toss broccoli with olive oil, salt, pepper and sliced garlic. (You should not use an expensive extra-virgin oil in this step; all the volatiles that make it special will cook out.) Roast 20-25 min until crisp-tender, and the edges of the florets are beginning to brown. Shake the pan occasionally.
Add lemon zest, lemon juice, olive oil (here is where you break out the high-quality super-flavorful stuff), pine nuts, Parmigiano and basil. Toss thoroughly and serve hot.