Preheat oven to 425°. Cut broccoli crowns into quarters from top to bottom. Drizzle with oil; sprinkle with salt, pepper and pepper flakes. Place in a parchment-lined 15x10x1-in. pan.
Roast until crisp and tender, 10-12 minutes. Sprinkle with garlic; roast 5 minutes longer. Sprinkle with cheese; roast until cheese is melted and stalks of broccoli are tender, 2-4 minutes more. Sprinkle with lemon zest.