In a large saute pan, heat the olive oil, garlic, and pepper flakes over medium heat until fragrant. Once the garlic has turned golden in color, remove it from the pan. You are left with garlic-infused oil in the pan. Add the broccoli to the pan.
Cook's Note: Be sure the broccoli is completely dry before tossing it into the pan.
Toss the broccoli to coat with the oil. Season with salt and pepper and saute over medium heat until the broccoli barely loses some of its crunch, about 5 minutes. Turn the heat up to high and deglaze the pan with the red wine vinegar. Add a few tablespoons of water, if needed.
Cook's Note: Use pasta water if the pasta was made fresh.
Add in the pasta and toss to coat with the oil. Top with Parmesan cheese for serving.