Bring a large pot of salted water to a rolling boil.
Add pasta to the boiling water and cook according to package instructions, typically 9 to 11 minutes.
Add frozen broccoli florets to the boiling pasta water during the final 3 minutes of the pasta cook time.
Reserve 1/2 cup of the starchy pasta water, then drain the pasta and broccoli together.
In the same pot, heat olive oil over medium heat. Sauté minced garlic and red pepper flakes for 60 seconds until fragrant.
Add the shredded rotisserie chicken to the pot and stir for 2 minutes to heat through.
Return the pasta and broccoli to the pot, tossing to combine with the garlic oil and chicken.
Gradually add the Parmesan cheese and the reserved pasta water, stirring constantly until a light emulsified sauce forms.
Season with salt and black pepper. Serve immediately.