01 - Bring a large pot of salted water to a boil. Add pasta and cook according to package instructions, adding broccoli florets during the last 3 minutes. Drain and set aside.
02 - In a large skillet over medium heat, melt butter. Add minced garlic and sauté for 1 minute until fragrant.
03 - Sprinkle flour over butter and garlic, whisking constantly for 1 minute to form a roux.
04 - Gradually whisk in milk, continuing to cook and stir frequently until sauce thickens, approximately 3–4 minutes.
05 - Stir in Parmesan, salt, black pepper, and red pepper flakes. Cook for another minute until cheese melts and sauce becomes smooth.
06 - Add shredded chicken, drained pasta, and broccoli to skillet. Toss everything together until well coated and heated through, about 2–3 minutes.
07 - Taste and adjust seasoning if necessary. Serve hot, garnished with fresh parsley and additional Parmesan.