Preheat the oven to 425 degrees.
Cut the broccoli florets from the stalks and leave an inch or two of stalk attached to the florets. Discard the rest of the stalk or toss it in a freezer bag and into the freezer for when you need to make vegetable stock.
Cut the florets apart with a small knife and you should end up with about 8 cups of florets.
On a large sheet pan lined with aluminum foil, parchment paper or reusable silpat, arrange the florets so they are in a single layer. Add the sliced garlic and then drizzle 5 tablespoons olive oil. Toss well to combine. Sprinkle with salt and pepper.
Roast in the oven 20-25 minutes, until crisp-tender and the tips of some of the florets are browned. While the broccoli is cooking, zest the lemons and then juice them and set aside. Grate the Parmesan, if using.
When the broccoli is cooked to your liking, remove the pan from the oven and immediately toss with the remaining 1 1/2 tablespoons of olive oil, lemon juice, lemon zest and Parmesan. Serve immediately.