Cook broccoli in a large pot of boiling salted water for 4 minutes, until bright green and crisp-tender. Drain in a colander, return to pot, cover, and keep warm.
Meanwhile, heat olive oil, garlic, salt, and red pepper in a large skillet over medium-high heat, 1 minute, until garlic begins to sizzle. Stir in breadcrumbs, increase the heat to medium, and cook, stirring frequently, for 2 1/2 minutes, until crumbs are lightly toasted.
Transfer the broccoli to a serving bowl, add the crumb mixture and Parmesan, and toss until the broccoli is evenly coated. Serve hot.