Preheat oven to 425 degrees.
Cut the broccoli florets into bite-sized pieces and the stalks into very thin (1/8-inch) rounds. In a medium-sized mixing bowl, combine broccoli, garlic, salt, pepper, red pepper flakes, bread crumbs, and olive oil. Mix well.
Spread broccoli mixture onto a cookie sheet and place in the oven for 8 to 10 minutes. Meanwhile, heat a sauté pan to medium heat and toast pine nuts for about 3 minutes.
Remove broccoli from the oven, toss in the cheese and pine nuts, and place mixture in a serving dish. Drizzle balsamic vinegar over the broccoli and serve immediately.