Heat oven to 425°F. Place a rimmed baking sheet on the middle rack while it heats.
Trim stems, remove any tough outer leaves, and halve the Brussels sprouts. Pat them very dry.
Toss sprouts with olive oil, garlic, salt, and pepper in a large bowl until coated.
Spread sprouts on the hot baking sheet, cut sides down, in a single layer.
Roast 15 minutes. Stir and roast 7–10 minutes more, until browned and tender.
Finish with lemon juice. Toss with Parmesan and red pepper flakes if using, then serve hot.