Cut the stem ends off of the brussels sprouts. If they are small, cut them in half. If they are larger, cut them into quarters. (The goal is to chop the pieces as equal in size as possible.)
Place chopped brussels sprouts into a large bowl. Add chopped onion, smashed garlic cloves, and crushed red pepper. Drizzle on olive oil, then use tongs to toss the ingredients together. Sprinkle with salt and pepper, then toss again.
Spread the brussels sprouts out onto a small rimmed baking sheet (about 9" x 7"). Pop it into the oven, and cook for 15 minutes at 425. Carefully remove the pan from the oven, sprinkle with parmesan, and use tongs to toss the brussels sprouts with parmesan. Return to the oven, and cook another 8-10 minutes until tender.
Remove from the oven, and squeeze fresh lemon over the sprouts. Toss with tongs again, and serve immediately.