Move oven rack to middle position and preheat to 425 degrees F.
On a baking sheet, use your hands to toss the broccoli florets with olive oil, minced garlic, lemon zest, and 1/4 teaspoon of salt and pepper until the florets are evenly coated.
Arrange the broccoli florets so they are in a single layer on your baking sheet.
Roast the broccoli in the preheated oven for 15-20 minutes, or until broccoli is cooked through and beginning to brown on some of the edges (you can tell the broccoli is done when it is easily pierced with a fork).
Sprinkle the broccoli with salt and pepper to taste. Finally, sprinkle the Parmesan cheese over the florets and serve!