Bring a large pot of salted water to a boil. Add pasta and cook according to package directions until al dente, usually 10-12 minutes. In the last 3-4 minutes of cooking, add broccoli florets directly to the pasta water. Before draining, scoop out and save 1 cup of starchy pasta water—this is crucial for the creamy sauce. Drain pasta and broccoli together in a colander.

While pasta cooks, melt butter in a large skillet over medium heat. Add minced garlic and cook until fragrant, about 1 minute—don't let it burn or it'll taste bitter. Pour in heavy cream and bring to a gentle simmer. Add Italian seasoning, red pepper flakes if using, salt, and black pepper. Let the sauce simmer for 2-3 minutes until it starts to thicken slightly.

Reduce heat to medium-low. Add shredded rotisserie chicken to the creamy sauce and stir to coat everything. Sprinkle in grated Parmesan cheese gradually while stirring constantly—this prevents clumping. The cheese will melt into the sauce creating that silky Alfredo texture. If sauce gets too thick, add splashes of reserved pasta water until you reach desired consistency.

Add drained pasta and broccoli to the skillet with the creamy chicken sauce. Toss everything together gently until every piece of pasta is coated in that gorgeous creamy garlic Parmesan sauce. Add more pasta water if needed to keep it saucy. Taste and adjust salt and pepper. Serve immediately garnished with fresh parsley and extra Parmesan cheese. The rotisserie chicken broccoli pasta is best enjoyed hot when the sauce is still creamy.