Bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente, usually 8-10 minutes. Add broccoli florets during the final 3 minutes of cooking time.
While pasta cooks, prepare the beef. Season sliced beef with salt and pepper. Heat 2 tablespoons olive oil in a large skillet over high heat until shimmering.
Sear the beef in a single layer for 1-2 minutes per side until browned but still slightly pink inside. Work in batches if needed to avoid overcrowding. Remove beef to a plate and set aside.
Reduce heat to medium and add remaining tablespoon of olive oil to the same skillet. Add minced garlic and cook for 30 seconds until fragrant.
Reserve 1/4 cup pasta water before draining. Drain the pasta and broccoli, then add them directly to the skillet with the garlic.
Return beef to the skillet along with any accumulated juices. Add lemon zest, lemon juice, and reserved pasta water, tossing everything together.
Sprinkle in Parmesan cheese and red pepper flakes (if using), stirring until the cheese melts and creates a light sauce that coats everything evenly.
Taste and adjust seasoning with salt and pepper as needed. Serve immediately topped with fresh parsley and additional Parmesan cheese.