Place the Broccoli, and Garlic in a bowl, add Salt, and Pepper, toss to evenly distribute. Add 2/3 of the Oil, toss to coat Broccoli evenly. On a baking sheet lined with parchment paper, place a rack. Place Broccoli on rack in a single layer.
Roast for 25 minutes, (until crisp-tender and the tips of some of the florets are browned).
Place Broccoli in a bowl, Add Lime Zest and Juice, toss to mix. Add rest of the Oil, toss to mix. Add Parmesan, toss to coat evenly.