Preheat oven to 400°F. Toss broccoli with 2 tablespoons oil on a rimmed baking sheet; brush cut sides of lemon with remaining 1/2 tablespoon oil. Season broccoli liberally with salt and pepper and sprinkle with red pepper flakes. Spread on baking sheet in a single layer. Put lemon halves on each end of pan, cut side up.
Roast, turning once, until broccoli is crisp-tender and lemons are soft and golden brown on top, about 20 minutes. Remove baking sheet from oven, squeeze juice from lemons over florets, and toss to coat. Sprinkle cheese over top and return to oven for 5 minutes longer. Serve hot or at room temperature.