Cook the pasta according to package instructions.
In a large skillet, heat olive oil over medium heat.
Add the chicken and cook until browned and cooked through, about 5-7 minutes.
Stir in minced garlic and red pepper flakes, cooking for an additional minute.
Add broccoli to the skillet and pour in the chicken broth; cover and steam for 3-5 minutes.
Slice the cooked chicken and mix it back into the skillet with the broccoli and garlic mixture.
Add the cooked pasta to the skillet and toss everything together, adjusting with reserved pasta water if necessary.
Finish with Parmesan cheese, salt, and pepper to taste before serving.